5 example of hypothesis and conclusion

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How to Write Hypothesis Test Conclusions (With Examples)

A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

Null Hypothesis (H 0 ): The sample data occurs purely from chance.
Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

Whether we reject or fail to reject the null hypothesis.
The significance level.
A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.

He performs a hypothesis test at a 10% significance level using the following hypotheses:

H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

Published by Zach

How to Write Hypothesis Test Conclusions (With Examples)

A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

Null Hypothesis (H 0 ): The sample data occurs purely from chance.
Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

Whether we reject or fail to reject the null hypothesis.
The significance level.
A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

He performs a hypothesis test at a 10% significance level using the following hypotheses:

H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

10 Examples of Using Probability in Real Life

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
Education : “Implementing a new teaching method will result in higher student achievement scores.”
Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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The Craft of Writing a Strong Hypothesis

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

A research hypothesis has to be simple yet clear to look justifiable enough.
It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1. Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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How to Write a Great Hypothesis

Hypothesis Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk, "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

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Hypothesis Format

Falsifiability of a hypothesis, operational definitions, types of hypotheses, hypotheses examples.

Collecting Data

Frequently Asked Questions

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

Forming a question
Performing background research
Creating a hypothesis
Designing an experiment
Collecting data
Analyzing the results
Drawing conclusions
Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. It is only at this point that researchers begin to develop a testable hypothesis. Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore a number of factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk wisdom that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

Is your hypothesis based on your research on a topic?
Can your hypothesis be tested?
Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the journal articles you read . Many authors will suggest questions that still need to be explored.

To form a hypothesis, you should take these steps:

Collect as many observations about a topic or problem as you can.
Evaluate these observations and look for possible causes of the problem.
Create a list of possible explanations that you might want to explore.
After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method , falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that if something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in a number of different ways. One of the basic principles of any type of scientific research is that the results must be replicable. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. How would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

Hypothesis Checklist

Does your hypothesis focus on something that you can actually test?
Does your hypothesis include both an independent and dependent variable?
Can you manipulate the variables?
Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

Simple hypothesis : This type of hypothesis suggests that there is a relationship between one independent variable and one dependent variable.
Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative sample of the population and then generalizes the findings to the larger group.
Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

"Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
Complex hypothesis: "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."
"Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."

Examples of a complex hypothesis include:

"People with high-sugar diets and sedentary activity levels are more likely to develop depression."
"Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

"Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
"There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

"Children who receive a new reading intervention will perform better than students who did not receive the intervention."
"Adults will perform better on a memory task than children."

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as case studies , naturalistic observations , and surveys are often used when it would be impossible or difficult to conduct an experiment . These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can then be used to look at how the variables are related. This type of research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually cause another to change.

A Word From Verywell

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Some examples of how to write a hypothesis include:

"Staying up late will lead to worse test performance the next day."
"People who consume one apple each day will visit the doctor fewer times each year."
"Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

The research question
The independent variable (IV)
The dependent variable (DV)
The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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How to Write a Research Hypothesis: Good & Bad Examples

What is a research hypothesis?

A research hypothesis is an attempt at explaining a phenomenon or the relationships between phenomena/variables in the real world. Hypotheses are sometimes called “educated guesses”, but they are in fact (or let’s say they should be) based on previous observations, existing theories, scientific evidence, and logic. A research hypothesis is also not a prediction—rather, predictions are ( should be) based on clearly formulated hypotheses. For example, “We tested the hypothesis that KLF2 knockout mice would show deficiencies in heart development” is an assumption or prediction, not a hypothesis.

The research hypothesis at the basis of this prediction is “the product of the KLF2 gene is involved in the development of the cardiovascular system in mice”—and this hypothesis is probably (hopefully) based on a clear observation, such as that mice with low levels of Kruppel-like factor 2 (which KLF2 codes for) seem to have heart problems. From this hypothesis, you can derive the idea that a mouse in which this particular gene does not function cannot develop a normal cardiovascular system, and then make the prediction that we started with.

What is the difference between a hypothesis and a prediction?

You might think that these are very subtle differences, and you will certainly come across many publications that do not contain an actual hypothesis or do not make these distinctions correctly. But considering that the formulation and testing of hypotheses is an integral part of the scientific method, it is good to be aware of the concepts underlying this approach. The two hallmarks of a scientific hypothesis are falsifiability (an evaluation standard that was introduced by the philosopher of science Karl Popper in 1934) and testability —if you cannot use experiments or data to decide whether an idea is true or false, then it is not a hypothesis (or at least a very bad one).

So, in a nutshell, you (1) look at existing evidence/theories, (2) come up with a hypothesis, (3) make a prediction that allows you to (4) design an experiment or data analysis to test it, and (5) come to a conclusion. Of course, not all studies have hypotheses (there is also exploratory or hypothesis-generating research), and you do not necessarily have to state your hypothesis as such in your paper.

But for the sake of understanding the principles of the scientific method, let’s first take a closer look at the different types of hypotheses that research articles refer to and then give you a step-by-step guide for how to formulate a strong hypothesis for your own paper.

Types of Research Hypotheses

Hypotheses can be simple , which means they describe the relationship between one single independent variable (the one you observe variations in or plan to manipulate) and one single dependent variable (the one you expect to be affected by the variations/manipulation). If there are more variables on either side, you are dealing with a complex hypothesis. You can also distinguish hypotheses according to the kind of relationship between the variables you are interested in (e.g., causal or associative ). But apart from these variations, we are usually interested in what is called the “alternative hypothesis” and, in contrast to that, the “null hypothesis”. If you think these two should be listed the other way round, then you are right, logically speaking—the alternative should surely come second. However, since this is the hypothesis we (as researchers) are usually interested in, let’s start from there.

Alternative Hypothesis

If you predict a relationship between two variables in your study, then the research hypothesis that you formulate to describe that relationship is your alternative hypothesis (usually H1 in statistical terms). The goal of your hypothesis testing is thus to demonstrate that there is sufficient evidence that supports the alternative hypothesis, rather than evidence for the possibility that there is no such relationship. The alternative hypothesis is usually the research hypothesis of a study and is based on the literature, previous observations, and widely known theories.

Null Hypothesis

The hypothesis that describes the other possible outcome, that is, that your variables are not related, is the null hypothesis ( H0 ). Based on your findings, you choose between the two hypotheses—usually that means that if your prediction was correct, you reject the null hypothesis and accept the alternative. Make sure, however, that you are not getting lost at this step of the thinking process: If your prediction is that there will be no difference or change, then you are trying to find support for the null hypothesis and reject H1.

Directional Hypothesis

While the null hypothesis is obviously “static”, the alternative hypothesis can specify a direction for the observed relationship between variables—for example, that mice with higher expression levels of a certain protein are more active than those with lower levels. This is then called a one-tailed hypothesis.

Another example for a directional one-tailed alternative hypothesis would be that

H1: Attending private classes before important exams has a positive effect on performance.

Your null hypothesis would then be that

H0: Attending private classes before important exams has no/a negative effect on performance.

Nondirectional Hypothesis

A nondirectional hypothesis does not specify the direction of the potentially observed effect, only that there is a relationship between the studied variables—this is called a two-tailed hypothesis. For instance, if you are studying a new drug that has shown some effects on pathways involved in a certain condition (e.g., anxiety) in vitro in the lab, but you can’t say for sure whether it will have the same effects in an animal model or maybe induce other/side effects that you can’t predict and potentially increase anxiety levels instead, you could state the two hypotheses like this:

H1: The only lab-tested drug (somehow) affects anxiety levels in an anxiety mouse model.

You then test this nondirectional alternative hypothesis against the null hypothesis:

H0: The only lab-tested drug has no effect on anxiety levels in an anxiety mouse model.

How to Write a Hypothesis for a Research Paper

Now that we understand the important distinctions between different kinds of research hypotheses, let’s look at a simple process of how to write a hypothesis.

Writing a Hypothesis Step:1

Ask a question, based on earlier research. Research always starts with a question, but one that takes into account what is already known about a topic or phenomenon. For example, if you are interested in whether people who have pets are happier than those who don’t, do a literature search and find out what has already been demonstrated. You will probably realize that yes, there is quite a bit of research that shows a relationship between happiness and owning a pet—and even studies that show that owning a dog is more beneficial than owning a cat ! Let’s say you are so intrigued by this finding that you wonder:

What is it that makes dog owners even happier than cat owners?

Let’s move on to Step 2 and find an answer to that question.

Writing a Hypothesis Step 2:

Formulate a strong hypothesis by answering your own question. Again, you don’t want to make things up, take unicorns into account, or repeat/ignore what has already been done. Looking at the dog-vs-cat papers your literature search returned, you see that most studies are based on self-report questionnaires on personality traits, mental health, and life satisfaction. What you don’t find is any data on actual (mental or physical) health measures, and no experiments. You therefore decide to make a bold claim come up with the carefully thought-through hypothesis that it’s maybe the lifestyle of the dog owners, which includes walking their dog several times per day, engaging in fun and healthy activities such as agility competitions, and taking them on trips, that gives them that extra boost in happiness. You could therefore answer your question in the following way:

Dog owners are happier than cat owners because of the dog-related activities they engage in.

Now you have to verify that your hypothesis fulfills the two requirements we introduced at the beginning of this resource article: falsifiability and testability . If it can’t be wrong and can’t be tested, it’s not a hypothesis. We are lucky, however, because yes, we can test whether owning a dog but not engaging in any of those activities leads to lower levels of happiness or well-being than owning a dog and playing and running around with them or taking them on trips.

Writing a Hypothesis Step 3:

Make your predictions and define your variables. We have verified that we can test our hypothesis, but now we have to define all the relevant variables, design our experiment or data analysis, and make precise predictions. You could, for example, decide to study dog owners (not surprising at this point), let them fill in questionnaires about their lifestyle as well as their life satisfaction (as other studies did), and then compare two groups of active and inactive dog owners. Alternatively, if you want to go beyond the data that earlier studies produced and analyzed and directly manipulate the activity level of your dog owners to study the effect of that manipulation, you could invite them to your lab, select groups of participants with similar lifestyles, make them change their lifestyle (e.g., couch potato dog owners start agility classes, very active ones have to refrain from any fun activities for a certain period of time) and assess their happiness levels before and after the intervention. In both cases, your independent variable would be “ level of engagement in fun activities with dog” and your dependent variable would be happiness or well-being .

Examples of a Good and Bad Hypothesis

Let’s look at a few examples of good and bad hypotheses to get you started.

Good Hypothesis Examples

Bad hypothesis examples, tips for writing a research hypothesis.

If you understood the distinction between a hypothesis and a prediction we made at the beginning of this article, then you will have no problem formulating your hypotheses and predictions correctly. To refresh your memory: We have to (1) look at existing evidence, (2) come up with a hypothesis, (3) make a prediction, and (4) design an experiment. For example, you could summarize your dog/happiness study like this:

(1) While research suggests that dog owners are happier than cat owners, there are no reports on what factors drive this difference. (2) We hypothesized that it is the fun activities that many dog owners (but very few cat owners) engage in with their pets that increases their happiness levels. (3) We thus predicted that preventing very active dog owners from engaging in such activities for some time and making very inactive dog owners take up such activities would lead to an increase and decrease in their overall self-ratings of happiness, respectively. (4) To test this, we invited dog owners into our lab, assessed their mental and emotional well-being through questionnaires, and then assigned them to an “active” and an “inactive” group, depending on…

Note that you use “we hypothesize” only for your hypothesis, not for your experimental prediction, and “would” or “if – then” only for your prediction, not your hypothesis. A hypothesis that states that something “would” affect something else sounds as if you don’t have enough confidence to make a clear statement—in which case you can’t expect your readers to believe in your research either. Write in the present tense, don’t use modal verbs that express varying degrees of certainty (such as may, might, or could ), and remember that you are not drawing a conclusion while trying not to exaggerate but making a clear statement that you then, in a way, try to disprove . And if that happens, that is not something to fear but an important part of the scientific process.

Similarly, don’t use “we hypothesize” when you explain the implications of your research or make predictions in the conclusion section of your manuscript, since these are clearly not hypotheses in the true sense of the word. As we said earlier, you will find that many authors of academic articles do not seem to care too much about these rather subtle distinctions, but thinking very clearly about your own research will not only help you write better but also ensure that even that infamous Reviewer 2 will find fewer reasons to nitpick about your manuscript.

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Now that you know how to write a strong research hypothesis for your research paper, you might be interested in our free AI proofreader , Wordvice AI, which finds and fixes errors in grammar, punctuation, and word choice in academic texts. Or if you are interested in human proofreading , check out our English editing services , including research paper editing and manuscript editing .

On the Wordvice academic resources website , you can also find many more articles and other resources that can help you with writing the other parts of your research paper , with making a research paper outline before you put everything together, or with writing an effective cover letter once you are ready to submit.

The Scientific Method by Science Made Simple

Understanding and using the scientific method.

The Scientific Method is a process used to design and perform experiments. It's important to minimize experimental errors and bias, and increase confidence in the accuracy of your results.

In the previous sections, we talked about how to pick a good topic and specific question to investigate. Now we will discuss how to carry out your investigation.

Steps of the Scientific Method

Observation/Research
Experimentation

Now that you have settled on the question you want to ask, it's time to use the Scientific Method to design an experiment to answer that question.

If your experiment isn't designed well, you may not get the correct answer. You may not even get any definitive answer at all!

The Scientific Method is a logical and rational order of steps by which scientists come to conclusions about the world around them. The Scientific Method helps to organize thoughts and procedures so that scientists can be confident in the answers they find.

OBSERVATION is first step, so that you know how you want to go about your research.

HYPOTHESIS is the answer you think you'll find.

PREDICTION is your specific belief about the scientific idea: If my hypothesis is true, then I predict we will discover this.

EXPERIMENT is the tool that you invent to answer the question, and

CONCLUSION is the answer that the experiment gives.

Don't worry, it isn't that complicated. Let's take a closer look at each one of these steps. Then you can understand the tools scientists use for their science experiments, and use them for your own.

OBSERVATION

This step could also be called "research." It is the first stage in understanding the problem.

After you decide on topic, and narrow it down to a specific question, you will need to research everything that you can find about it. You can collect information from your own experiences, books, the internet, or even smaller "unofficial" experiments.

Let's continue the example of a science fair idea about tomatoes in the garden. You like to garden, and notice that some tomatoes are bigger than others and wonder why.

Because of this personal experience and an interest in the problem, you decide to learn more about what makes plants grow.

For this stage of the Scientific Method, it's important to use as many sources as you can find. The more information you have on your science fair topic, the better the design of your experiment is going to be, and the better your science fair project is going to be overall.

Also try to get information from your teachers or librarians, or professionals who know something about your science fair project. They can help to guide you to a solid experimental setup.

The next stage of the Scientific Method is known as the "hypothesis." This word basically means "a possible solution to a problem, based on knowledge and research."

The hypothesis is a simple statement that defines what you think the outcome of your experiment will be.

All of the first stage of the Scientific Method -- the observation, or research stage -- is designed to help you express a problem in a single question ("Does the amount of sunlight in a garden affect tomato size?") and propose an answer to the question based on what you know. The experiment that you will design is done to test the hypothesis.

Using the example of the tomato experiment, here is an example of a hypothesis:

TOPIC: "Does the amount of sunlight a tomato plant receives affect the size of the tomatoes?"

HYPOTHESIS: "I believe that the more sunlight a tomato plant receives, the larger the tomatoes will grow.

This hypothesis is based on:

(1) Tomato plants need sunshine to make food through photosynthesis, and logically, more sun means more food, and;

(2) Through informal, exploratory observations of plants in a garden, those with more sunlight appear to grow bigger.

The hypothesis is your general statement of how you think the scientific phenomenon in question works.

Your prediction lets you get specific -- how will you demonstrate that your hypothesis is true? The experiment that you will design is done to test the prediction.

An important thing to remember during this stage of the scientific method is that once you develop a hypothesis and a prediction, you shouldn't change it, even if the results of your experiment show that you were wrong.

An incorrect prediction does NOT mean that you "failed." It just means that the experiment brought some new facts to light that maybe you hadn't thought about before.

Continuing our tomato plant example, a good prediction would be: Increasing the amount of sunlight tomato plants in my experiment receive will cause an increase in their size compared to identical plants that received the same care but less light.

This is the part of the scientific method that tests your hypothesis. An experiment is a tool that you design to find out if your ideas about your topic are right or wrong.

It is absolutely necessary to design a science fair experiment that will accurately test your hypothesis. The experiment is the most important part of the scientific method. It's the logical process that lets scientists learn about the world.

On the next page, we'll discuss the ways that you can go about designing a science fair experiment idea.

The final step in the scientific method is the conclusion. This is a summary of the experiment's results, and how those results match up to your hypothesis.

You have two options for your conclusions: based on your results, either:

(1) YOU CAN REJECT the hypothesis, or

(2) YOU CAN NOT REJECT the hypothesis.

This is an important point!

You can not PROVE the hypothesis with a single experiment, because there is a chance that you made an error somewhere along the way.

What you can say is that your results SUPPORT the original hypothesis.

If your original hypothesis didn't match up with the final results of your experiment, don't change the hypothesis.

Instead, try to explain what might have been wrong with your original hypothesis. What information were you missing when you made your prediction? What are the possible reasons the hypothesis and experimental results didn't match up?

Remember, a science fair experiment isn't a failure simply because does not agree with your hypothesis. No one will take points off if your prediction wasn't accurate. Many important scientific discoveries were made as a result of experiments gone wrong!

A science fair experiment is only a failure if its design is flawed. A flawed experiment is one that (1) doesn't keep its variables under control, and (2) doesn't sufficiently answer the question that you asked of it.

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Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, Ph.D., is a qualified psychology teacher with over 18 years experience of working in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

15 Hypothesis Examples

hypothesis definition and example, explained below

A hypothesis is defined as a testable prediction , and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022).

In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis (which makes a prediction about an effect of a treatment will be positive or negative) and the associative hypothesis (which makes a prediction about the association between two variables).

This article will dive into some interesting examples of hypotheses and examine potential ways you might test each one.

Hypothesis Examples

1. “inadequate sleep decreases memory retention”.

Field: Psychology

Type: Causal Hypothesis A causal hypothesis explores the effect of one variable on another. This example posits that a lack of adequate sleep causes decreased memory retention. In other words, if you are not getting enough sleep, your ability to remember and recall information may suffer.

How to Test:

To test this hypothesis, you might devise an experiment whereby your participants are divided into two groups: one receives an average of 8 hours of sleep per night for a week, while the other gets less than the recommended sleep amount.

During this time, all participants would daily study and recall new, specific information. You’d then measure memory retention of this information for both groups using standard memory tests and compare the results.

Should the group with less sleep have statistically significant poorer memory scores, the hypothesis would be supported.

Ensuring the integrity of the experiment requires taking into account factors such as individual health differences, stress levels, and daily nutrition.

Relevant Study: Sleep loss, learning capacity and academic performance (Curcio, Ferrara & De Gennaro, 2006)

2. “Increase in Temperature Leads to Increase in Kinetic Energy”

Field: Physics

Type: Deductive Hypothesis The deductive hypothesis applies the logic of deductive reasoning – it moves from a general premise to a more specific conclusion. This specific hypothesis assumes that as temperature increases, the kinetic energy of particles also increases – that is, when you heat something up, its particles move around more rapidly.

This hypothesis could be examined by heating a gas in a controlled environment and capturing the movement of its particles as a function of temperature.

You’d gradually increase the temperature and measure the kinetic energy of the gas particles with each increment. If the kinetic energy consistently rises with the temperature, your hypothesis gets supporting evidence.

Variables such as pressure and volume of the gas would need to be held constant to ensure validity of results.

3. “Children Raised in Bilingual Homes Develop Better Cognitive Skills”

Field: Psychology/Linguistics

Type: Comparative Hypothesis The comparative hypothesis posits a difference between two or more groups based on certain variables. In this context, you might propose that children raised in bilingual homes have superior cognitive skills compared to those raised in monolingual homes.

Testing this hypothesis could involve identifying two groups of children: those raised in bilingual homes, and those raised in monolingual homes.

Cognitive skills in both groups would be evaluated using a standard cognitive ability test at different stages of development. The examination would be repeated over a significant time period for consistency.

If the group raised in bilingual homes persistently scores higher than the other, the hypothesis would thereby be supported.

The challenge for the researcher would be controlling for other variables that could impact cognitive development, such as socio-economic status, education level of parents, and parenting styles.

Relevant Study: The cognitive benefits of being bilingual (Marian & Shook, 2012)

4. “High-Fiber Diet Leads to Lower Incidences of Cardiovascular Diseases”

Field: Medicine/Nutrition

Type: Alternative Hypothesis The alternative hypothesis suggests an alternative to a null hypothesis. In this context, the implied null hypothesis could be that diet has no effect on cardiovascular health, which the alternative hypothesis contradicts by suggesting that a high-fiber diet leads to fewer instances of cardiovascular diseases.

To test this hypothesis, a longitudinal study could be conducted on two groups of participants; one adheres to a high-fiber diet, while the other follows a diet low in fiber.

After a fixed period, the cardiovascular health of participants in both groups could be analyzed and compared. If the group following a high-fiber diet has a lower number of recorded cases of cardiovascular diseases, it would provide evidence supporting the hypothesis.

Control measures should be implemented to exclude the influence of other lifestyle and genetic factors that contribute to cardiovascular health.

Relevant Study: Dietary fiber, inflammation, and cardiovascular disease (King, 2005)

5. “Gravity Influences the Directional Growth of Plants”

Field: Agronomy / Botany

Type: Explanatory Hypothesis An explanatory hypothesis attempts to explain a phenomenon. In this case, the hypothesis proposes that gravity affects how plants direct their growth – both above-ground (toward sunlight) and below-ground (towards water and other resources).

The testing could be conducted by growing plants in a rotating cylinder to create artificial gravity.

Observations on the direction of growth, over a specified period, can provide insights into the influencing factors. If plants consistently direct their growth in a manner that indicates the influence of gravitational pull, the hypothesis is substantiated.

It is crucial to ensure that other growth-influencing factors, such as light and water, are uniformly distributed so that only gravity influences the directional growth.

6. “The Implementation of Gamified Learning Improves Students’ Motivation”

Field: Education

Type: Relational Hypothesis The relational hypothesis describes the relation between two variables. Here, the hypothesis is that the implementation of gamified learning has a positive effect on the motivation of students.

To validate this proposition, two sets of classes could be compared: one that implements a learning approach with game-based elements, and another that follows a traditional learning approach.

The students’ motivation levels could be gauged by monitoring their engagement, performance, and feedback over a considerable timeframe.

If the students engaged in the gamified learning context present higher levels of motivation and achievement, the hypothesis would be supported.

Control measures ought to be put into place to account for individual differences, including prior knowledge and attitudes towards learning.

Relevant Study: Does educational gamification improve students’ motivation? (Chapman & Rich, 2018)

7. “Mathematics Anxiety Negatively Affects Performance”

Field: Educational Psychology

Type: Research Hypothesis The research hypothesis involves making a prediction that will be tested. In this case, the hypothesis proposes that a student’s anxiety about math can negatively influence their performance in math-related tasks.

To assess this hypothesis, researchers must first measure the mathematics anxiety levels of a sample of students using a validated instrument, such as the Mathematics Anxiety Rating Scale.

Then, the students’ performance in mathematics would be evaluated through standard testing. If there’s a negative correlation between the levels of math anxiety and math performance (meaning as anxiety increases, performance decreases), the hypothesis would be supported.

It would be crucial to control for relevant factors such as overall academic performance and previous mathematical achievement.

8. “Disruption of Natural Sleep Cycle Impairs Worker Productivity”

Field: Organizational Psychology

Type: Operational Hypothesis The operational hypothesis involves defining the variables in measurable terms. In this example, the hypothesis posits that disrupting the natural sleep cycle, for instance through shift work or irregular working hours, can lessen productivity among workers.

To test this hypothesis, you could collect data from workers who maintain regular working hours and those with irregular schedules.

Measuring productivity could involve examining the worker’s ability to complete tasks, the quality of their work, and their efficiency.

If workers with interrupted sleep cycles demonstrate lower productivity compared to those with regular sleep patterns, it would lend support to the hypothesis.

Consideration should be given to potential confounding variables such as job type, worker age, and overall health.

9. “Regular Physical Activity Reduces the Risk of Depression”

Field: Health Psychology

Type: Predictive Hypothesis A predictive hypothesis involves making a prediction about the outcome of a study based on the observed relationship between variables. In this case, it is hypothesized that individuals who engage in regular physical activity are less likely to suffer from depression.

Longitudinal studies would suit to test this hypothesis, tracking participants’ levels of physical activity and their mental health status over time.

The level of physical activity could be self-reported or monitored, while mental health status could be assessed using standard diagnostic tools or surveys.

If data analysis shows that participants maintaining regular physical activity have a lower incidence of depression, this would endorse the hypothesis.

However, care should be taken to control other lifestyle and behavioral factors that could intervene with the results.

Relevant Study: Regular physical exercise and its association with depression (Kim, 2022)

10. “Regular Meditation Enhances Emotional Stability”

Type: Empirical Hypothesis In the empirical hypothesis, predictions are based on amassed empirical evidence . This particular hypothesis theorizes that frequent meditation leads to improved emotional stability, resonating with numerous studies linking meditation to a variety of psychological benefits.

Earlier studies reported some correlations, but to test this hypothesis directly, you’d organize an experiment where one group meditates regularly over a set period while a control group doesn’t.

Both groups’ emotional stability levels would be measured at the start and end of the experiment using a validated emotional stability assessment.

If regular meditators display noticeable improvements in emotional stability compared to the control group, the hypothesis gains credit.

You’d have to ensure a similar emotional baseline for all participants at the start to avoid skewed results.

11. “Children Exposed to Reading at an Early Age Show Superior Academic Progress”

Type: Directional Hypothesis The directional hypothesis predicts the direction of an expected relationship between variables. Here, the hypothesis anticipates that early exposure to reading positively affects a child’s academic advancement.

A longitudinal study tracking children’s reading habits from an early age and their consequent academic performance could validate this hypothesis.

Parents could report their children’s exposure to reading at home, while standardized school exam results would provide a measure of academic achievement.

If the children exposed to early reading consistently perform better acadically, it gives weight to the hypothesis.

However, it would be important to control for variables that might impact academic performance, such as socioeconomic background, parental education level, and school quality.

12. “Adopting Energy-efficient Technologies Reduces Carbon Footprint of Industries”

Field: Environmental Science

Type: Descriptive Hypothesis A descriptive hypothesis predicts the existence of an association or pattern related to variables. In this scenario, the hypothesis suggests that industries adopting energy-efficient technologies will resultantly show a reduced carbon footprint.

Global industries making use of energy-efficient technologies could track their carbon emissions over time. At the same time, others not implementing such technologies continue their regular tracking.

After a defined time, the carbon emission data of both groups could be compared. If industries that adopted energy-efficient technologies demonstrate a notable reduction in their carbon footprints, the hypothesis would hold strong.

In the experiment, you would exclude variations brought by factors such as industry type, size, and location.

13. “Reduced Screen Time Improves Sleep Quality”

Type: Simple Hypothesis The simple hypothesis is a prediction about the relationship between two variables, excluding any other variables from consideration. This example posits that by reducing time spent on devices like smartphones and computers, an individual should experience improved sleep quality.

A sample group would need to reduce their daily screen time for a pre-determined period. Sleep quality before and after the reduction could be measured using self-report sleep diaries and objective measures like actigraphy, monitoring movement and wakefulness during sleep.

If the data shows that sleep quality improved post the screen time reduction, the hypothesis would be validated.

Other aspects affecting sleep quality, like caffeine intake, should be controlled during the experiment.

Relevant Study: Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep (Waller et al., 2021)

14. Engaging in Brain-Training Games Improves Cognitive Functioning in Elderly

Field: Gerontology

Type: Inductive Hypothesis Inductive hypotheses are based on observations leading to broader generalizations and theories. In this context, the hypothesis deduces from observed instances that engaging in brain-training games can help improve cognitive functioning in the elderly.

A longitudinal study could be conducted where an experimental group of elderly people partakes in regular brain-training games.

Their cognitive functioning could be assessed at the start of the study and at regular intervals using standard neuropsychological tests.

If the group engaging in brain-training games shows better cognitive functioning scores over time compared to a control group not playing these games, the hypothesis would be supported.

15. Farming Practices Influence Soil Erosion Rates

Type: Null Hypothesis A null hypothesis is a negative statement assuming no relationship or difference between variables. The hypothesis in this context asserts there’s no effect of different farming practices on the rates of soil erosion.

Comparing soil erosion rates in areas with different farming practices over a considerable timeframe could help test this hypothesis.

If, statistically, the farming practices do not lead to differences in soil erosion rates, the null hypothesis is accepted.

However, if marked variation appears, the null hypothesis is rejected, meaning farming practices do influence soil erosion rates. It would be crucial to control for external factors like weather, soil type, and natural vegetation.

The variety of hypotheses mentioned above underscores the diversity of research constructs inherent in different fields, each with its unique purpose and way of testing.

While researchers may develop hypotheses primarily as tools to define and narrow the focus of the study, these hypotheses also serve as valuable guiding forces for the data collection and analysis procedures, making the research process more efficient and direction-focused.

Hypotheses serve as a compass for any form of academic research. The diverse examples provided, from Psychology to Educational Studies, Environmental Science to Gerontology, clearly demonstrate how certain hypotheses suit specific fields more aptly than others.

It is important to underline that although these varied hypotheses differ in their structure and methods of testing, each endorses the fundamental value of empiricism in research. Evidence-based decision making remains at the heart of scholarly inquiry, regardless of the research field, thus aligning all hypotheses to the core purpose of scientific investigation.

Testing hypotheses is an essential part of the scientific method . By doing so, researchers can either confirm their predictions, giving further validity to an existing theory, or they might uncover new insights that could potentially shift the field’s understanding of a particular phenomenon. In either case, hypotheses serve as the stepping stones for scientific exploration and discovery.

Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J. W., & Williams, R. A. (2021). SAGE research methods foundations . SAGE Publications Ltd.

Curcio, G., Ferrara, M., & De Gennaro, L. (2006). Sleep loss, learning capacity and academic performance. Sleep medicine reviews , 10 (5), 323-337.

Kim, J. H. (2022). Regular physical exercise and its association with depression: A population-based study short title: Exercise and depression. Psychiatry Research , 309 , 114406.

King, D. E. (2005). Dietary fiber, inflammation, and cardiovascular disease. Molecular nutrition & food research , 49 (6), 594-600.

Marian, V., & Shook, A. (2012, September). The cognitive benefits of being bilingual. In Cerebrum: the Dana forum on brain science (Vol. 2012). Dana Foundation.

Tan, W. C. K. (2022). Research Methods: A Practical Guide For Students And Researchers (Second Edition) . World Scientific Publishing Company.

Waller, N. A., Zhang, N., Cocci, A. H., D’Agostino, C., Wesolek‐Greenson, S., Wheelock, K., … & Resnicow, K. (2021). Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep. Child: care, health and development, 47 (5), 618-626.

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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How to State the Conclusion about a Hypothesis Test

After you have completed the statistical analysis and decided to reject or fail to reject the Null hypothesis, you need to state your conclusion about the claim. To get the correct wording, you need to recall which hypothesis was the claim.

If the claim was the null, then your conclusion is about whether there was sufficient evidence to reject the claim. Remember, we can never prove the null to be true, but failing to reject it is the next best thing. So, it is not correct to say, “Accept the Null.”

If the claim is the alternative hypothesis, your conclusion can be whether there was sufficient evidence to support (prove) the alternative is true.

Use the following table to help you make a good conclusion.

The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself.

For example, if the claim was the alternative that the mean score on a test was greater than 85, and your decision was to Reject then Null , then you could conclude: “ At the 5% significance level, there is sufficient evidence to support the claim that the mean score on the test was greater than 85. ”

The reason you should include the significance level is that the decision, and thus the conclusion, could be different if the significance level was not 5%.

If you are curious why we say “Fail to Reject the Null” instead of “Accept the Null,” this short video might be of interest: Here

2 thoughts on “How to State the Conclusion about a Hypothesis Test”

It is concluded that the null hypothesis Ho is not rejected proportion p is greater than 0.5, at the 0.05 significance

People living in rural Idaho community live longer than 77 years

AP®︎/College Statistics

Course: ap®︎/college statistics > unit 10.

Idea behind hypothesis testing
Examples of null and alternative hypotheses
Writing null and alternative hypotheses
P-values and significance tests
Comparing P-values to different significance levels
Estimating a P-value from a simulation
Estimating P-values from simulations

Using P-values to make conclusions

(Choice A) Fail to reject H 0 ‍ A Fail to reject H 0 ‍
(Choice B) Reject H 0 ‍ and accept H a ‍ B Reject H 0 ‍ and accept H a ‍
(Choice C) Accept H 0 ‍ C Accept H 0 ‍
(Choice A) The evidence suggests that these subjects can do better than guessing when identifying the bottled water. A The evidence suggests that these subjects can do better than guessing when identifying the bottled water.
(Choice B) We don't have enough evidence to say that these subjects can do better than guessing when identifying the bottled water. B We don't have enough evidence to say that these subjects can do better than guessing when identifying the bottled water.
(Choice C) The evidence suggests that these subjects were simply guessing when identifying the bottled water. C The evidence suggests that these subjects were simply guessing when identifying the bottled water.
(Choice A) She would have rejected H a ‍ . A She would have rejected H a ‍ .
(Choice B) She would have accepted H 0 ‍ . B She would have accepted H 0 ‍ .
(Choice C) She would have rejected H 0 ‍ and accepted H a ‍ . C She would have rejected H 0 ‍ and accepted H a ‍ .
(Choice D) She would have reached the same conclusion using either α = 0.05 ‍ or α = 0.10 ‍ . D She would have reached the same conclusion using either α = 0.05 ‍ or α = 0.10 ‍ .
(Choice A) The evidence suggests that these bags are being filled with a mean amount that is different than 7.4 kg ‍ . A The evidence suggests that these bags are being filled with a mean amount that is different than 7.4 kg ‍ .
(Choice B) We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4 kg ‍ . B We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4 kg ‍ .
(Choice C) The evidence suggests that these bags are being filled with a mean amount of 7.4 kg ‍ . C The evidence suggests that these bags are being filled with a mean amount of 7.4 kg ‍ .
(Choice A) They would have rejected H a ‍ . A They would have rejected H a ‍ .
(Choice B) They would have accepted H 0 ‍ . B They would have accepted H 0 ‍ .
(Choice C) They would have failed to reject H 0 ‍ . C They would have failed to reject H 0 ‍ .
(Choice D) They would have reached the same conclusion using either α = 0.05 ‍ or α = 0.01 ‍ . D They would have reached the same conclusion using either α = 0.05 ‍ or α = 0.01 ‍ .

Ethics and the significance level α ‍

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Dissertation

How to Write a Thesis or Dissertation Conclusion

Published on September 6, 2022 by Tegan George and Shona McCombes. Revised on November 20, 2023.

The conclusion is the very last part of your thesis or dissertation . It should be concise and engaging, leaving your reader with a clear understanding of your main findings, as well as the answer to your research question .

In it, you should:

Clearly state the answer to your main research question
Summarize and reflect on your research process
Make recommendations for future work on your thesis or dissertation topic
Show what new knowledge you have contributed to your field
Wrap up your thesis or dissertation

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Discussion vs. conclusion, how long should your conclusion be, step 1: answer your research question, step 2: summarize and reflect on your research, step 3: make future recommendations, step 4: emphasize your contributions to your field, step 5: wrap up your thesis or dissertation, full conclusion example, conclusion checklist, other interesting articles, frequently asked questions about conclusion sections.

While your conclusion contains similar elements to your discussion section , they are not the same thing.

Your conclusion should be shorter and more general than your discussion. Instead of repeating literature from your literature review , discussing specific research results , or interpreting your data in detail, concentrate on making broad statements that sum up the most important insights of your research.

As a rule of thumb, your conclusion should not introduce new data, interpretations, or arguments.

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Depending on whether you are writing a thesis or dissertation, your length will vary. Generally, a conclusion should make up around 5–7% of your overall word count.

An empirical scientific study will often have a short conclusion, concisely stating the main findings and recommendations for future research. A humanities dissertation topic or systematic review , on the other hand, might require more space to conclude its analysis, tying all the previous sections together in an overall argument.

Your conclusion should begin with the main question that your thesis or dissertation aimed to address. This is your final chance to show that you’ve done what you set out to do, so make sure to formulate a clear, concise answer.

Don’t repeat a list of all the results that you already discussed
Do synthesize them into a final takeaway that the reader will remember.

An empirical thesis or dissertation conclusion may begin like this:

A case study –based thesis or dissertation conclusion may begin like this:

In the second example, the research aim is not directly restated, but rather added implicitly to the statement. To avoid repeating yourself, it is helpful to reformulate your aims and questions into an overall statement of what you did and how you did it.

Your conclusion is an opportunity to remind your reader why you took the approach you did, what you expected to find, and how well the results matched your expectations.

To avoid repetition , consider writing more reflectively here, rather than just writing a summary of each preceding section. Consider mentioning the effectiveness of your methodology , or perhaps any new questions or unexpected insights that arose in the process.

You can also mention any limitations of your research, but only if you haven’t already included these in the discussion. Don’t dwell on them at length, though—focus on the positives of your work.

While x limits the generalizability of the results, this approach provides new insight into y .
This research clearly illustrates x , but it also raises the question of y .

Prevent plagiarism. Run a free check.

You may already have made a few recommendations for future research in your discussion section, but the conclusion is a good place to elaborate and look ahead, considering the implications of your findings in both theoretical and practical terms.

Based on these conclusions, practitioners should consider …
To better understand the implications of these results, future studies could address …
Further research is needed to determine the causes of/effects of/relationship between …

When making recommendations for further research, be sure not to undermine your own work. Relatedly, while future studies might confirm, build on, or enrich your conclusions, they shouldn’t be required for your argument to feel complete. Your work should stand alone on its own merits.

Just as you should avoid too much self-criticism, you should also avoid exaggerating the applicability of your research. If you’re making recommendations for policy, business, or other practical implementations, it’s generally best to frame them as “shoulds” rather than “musts.” All in all, the purpose of academic research is to inform, explain, and explore—not to demand.

Make sure your reader is left with a strong impression of what your research has contributed to the state of your field.

Some strategies to achieve this include:

Returning to your problem statement to explain how your research helps solve the problem
Referring back to the literature review and showing how you have addressed a gap in knowledge
Discussing how your findings confirm or challenge an existing theory or assumption

Again, avoid simply repeating what you’ve already covered in the discussion in your conclusion. Instead, pick out the most important points and sum them up succinctly, situating your project in a broader context.

The end is near! Once you’ve finished writing your conclusion, it’s time to wrap up your thesis or dissertation with a few final steps:

It’s a good idea to write your abstract next, while the research is still fresh in your mind.
Next, make sure your reference list is complete and correctly formatted. To speed up the process, you can use our free APA citation generator .
Once you’ve added any appendices , you can create a table of contents and title page .
Finally, read through the whole document again to make sure your thesis is clearly written and free from language errors. You can proofread it yourself , ask a friend, or consider Scribbr’s proofreading and editing service .

Here is an example of how you can write your conclusion section. Notice how it includes everything mentioned above:

V. Conclusion

The current research aimed to identify acoustic speech characteristics which mark the beginning of an exacerbation in COPD patients.

The central questions for this research were as follows: 1. Which acoustic measures extracted from read speech differ between COPD speakers in stable condition and healthy speakers? 2. In what ways does the speech of COPD patients during an exacerbation differ from speech of COPD patients during stable periods?

All recordings were aligned using a script. Subsequently, they were manually annotated to indicate respiratory actions such as inhaling and exhaling. The recordings of 9 stable COPD patients reading aloud were then compared with the recordings of 5 healthy control subjects reading aloud. The results showed a significant effect of condition on the number of in- and exhalations per syllable, the number of non-linguistic in- and exhalations per syllable, and the ratio of voiced and silence intervals. The number of in- and exhalations per syllable and the number of non-linguistic in- and exhalations per syllable were higher for COPD patients than for healthy controls, which confirmed both hypotheses.

However, the higher ratio of voiced and silence intervals for COPD patients compared to healthy controls was not in line with the hypotheses. This unpredicted result might have been caused by the different reading materials or recording procedures for both groups, or by a difference in reading skills. Moreover, there was a trend regarding the effect of condition on the number of syllables per breath group. The number of syllables per breath group was higher for healthy controls than for COPD patients, which was in line with the hypothesis. There was no effect of condition on pitch, intensity, center of gravity, pitch variability, speaking rate, or articulation rate.

This research has shown that the speech of COPD patients in exacerbation differs from the speech of COPD patients in stable condition. This might have potential for the detection of exacerbations. However, sustained vowels rarely occur in spontaneous speech. Therefore, the last two outcome measures might have greater potential for the detection of beginning exacerbations, but further research on the different outcome measures and their potential for the detection of exacerbations is needed due to the limitations of the current study.

Checklist: Conclusion

I have clearly and concisely answered the main research question .

I have summarized my overall argument or key takeaways.

I have mentioned any important limitations of the research.

I have given relevant recommendations .

I have clearly explained what my research has contributed to my field.

I have not introduced any new data or arguments.

You've written a great conclusion! Use the other checklists to further improve your dissertation.

If you want to know more about AI for academic writing, AI tools, or research bias, make sure to check out some of our other articles with explanations and examples or go directly to our tools!

Research bias

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In a thesis or dissertation, the discussion is an in-depth exploration of the results, going into detail about the meaning of your findings and citing relevant sources to put them in context.

The conclusion is more shorter and more general: it concisely answers your main research question and makes recommendations based on your overall findings.

While it may be tempting to present new arguments or evidence in your thesis or disseration conclusion , especially if you have a particularly striking argument you’d like to finish your analysis with, you shouldn’t. Theses and dissertations follow a more formal structure than this.

All your findings and arguments should be presented in the body of the text (more specifically in the discussion section and results section .) The conclusion is meant to summarize and reflect on the evidence and arguments you have already presented, not introduce new ones.

For a stronger dissertation conclusion , avoid including:

Important evidence or analysis that wasn’t mentioned in the discussion section and results section
Generic concluding phrases (e.g. “In conclusion …”)
Weak statements that undermine your argument (e.g., “There are good points on both sides of this issue.”)

Your conclusion should leave the reader with a strong, decisive impression of your work.

The conclusion of your thesis or dissertation shouldn’t take up more than 5–7% of your overall word count.

The conclusion of your thesis or dissertation should include the following:

A restatement of your research question
A summary of your key arguments and/or results
A short discussion of the implications of your research

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Module 8: Inference for One Proportion

Hypothesis testing (5 of 5), learning outcomes.

Recognize type I and type II errors.

What Can Go Wrong: Two Types of Errors

Statistical investigations involve making decisions in the face of uncertainty, so there is always some chance of making a wrong decision. In hypothesis testing, two types of wrong decisions can occur.

If the null hypothesis is true, but we reject it, the error is a type I error.

If the null hypothesis is false, but we fail to reject it, the error is a type II error.

The following table summarizes type I and II errors.

Hypothesis testing matrices. If we reject H null and H null is false, when we have correctly rejected the null hypothesis. If we reject H null and H null is tue, we have made a Type I error. If we accept H null and H null is trie, we have correct accepted the null hypothesis. If we accept H null and H null is false, we have made a Type II error.

Type I and type II errors are not caused by mistakes. These errors are the result of random chance. The data provide evidence for a conclusion that is false. It’s no one’s fault!

Data Use on Smart Phones

In a previous example, we looked at a hypothesis test about data usage on smart phones. The researcher investigated the claim that the mean data usage for all teens is greater than 62 MBs. The sample mean was 75 MBs. The P-value was approximately 0.023. In this situation, the P-value is the probability that we will get a sample mean of 75 MBs or higher if the true mean is 62 MBs.

Notice that the result (75 MBs) isn’t impossible, only very unusual. The result is rare enough that we question whether the null hypothesis is true. This is why we reject the null hypothesis. But it is possible that the null hypothesis hypothesis is true and the researcher happened to get a very unusual sample mean. In this case, the result is just due to chance, and the data have led to a type I error: rejecting the null hypothesis when it is actually true.

White Male Support for Obama in 2012

In a previous example, we conducted a hypothesis test using poll results to determine if white male support for Obama in 2012 will be less than 40%. Our poll of white males showed 35% planning to vote for Obama in 2012. Based on the sampling distribution, we estimated the P-value as 0.078. In this situation, the P-value is the probability that we will get a sample proportion of 0.35 or less if 0.40 of the population of white males support Obama.

At the 5% level, the poll did not give strong enough evidence for us to conclude that less than 40% of white males will vote for Obama in 2012.

Which type of error is possible in this situation? If, in fact, it is true that less than 40% of this population support Obama, then the data led to a type II error: failing to reject a null hypothesis that is false. In other words, we failed to accept an alternative hypothesis that is true.

We definitely did not make a type I error here because a type I error requires that we reject the null hypothesis.

What Is the Probability That We Will Make a Type I Error?

If the significance level is 5% (α = 0.05), then 5% of the time we will reject the null hypothesis (when it is true!). Of course we will not know if the null is true. But if it is, the natural variability that we expect in random samples will produce rare results 5% of the time. This makes sense because we assume the null hypothesis is true when we create the sampling distribution. We look at the variability in random samples selected from the population described by the null hypothesis.

Similarly, if the significance level is 1%, then 1% of the time sample results will be rare enough for us to reject the null hypothesis hypothesis. So if the null hypothesis is actually true, then by chance alone, 1% of the time we will reject a true null hypothesis. The probability of a type I error is therefore 1%.

In general, the probability of a type I error is α.

What Is the Probability That We Will Make a Type II Error?

The probability of a type I error, if the null hypothesis is true, is equal to the significance level. The probability of a type II error is much more complicated to calculate. We can reduce the risk of a type I error by using a lower significance level. The best way to reduce the risk of a type II error is by increasing the sample size. In theory, we could also increase the significance level, but doing so would increase the likelihood of a type I error at the same time. We discuss these ideas further in a later module.

A Fair Coin

In the long run, a fair coin lands heads up half of the time. (For this reason, a weighted coin is not fair.) We conducted a simulation in which each sample consists of 40 flips of a fair coin. Here is a simulated sampling distribution for the proportion of heads in 2,000 samples. Results ranged from 0.25 to 0.75.

A distribution bar graph with results ranging from 0.25 to 0.75. The center at 0.5 has the highest bar, and on either side the bars get lower. The graph is in the traditional bell curve shape, but with a slightly smaller slope on the left side of the peak.

In general, if the null hypothesis is true, the significance level gives the probability of making a type I error. If we conduct a large number of hypothesis tests using the same null hypothesis, then, a type I error will occur in a predictable percentage (α) of the hypothesis tests. This is a problem! If we run one hypothesis test and the data is significant at the 5% level, we have reasonably good evidence that the alternative hypothesis is true. If we run 20 hypothesis tests and the data in one of the tests is significant at the 5% level, it doesn’t tell us anything! We expect 5% of the tests (1 in 20) to show significant results just due to chance.

Cell Phones and Brain Cancer

The following is an excerpt from a 1999 New York Times article titled “Cell phones: questions but no answers,” as referenced by David S. Moore in Basic Practice of Statistics (4th ed., New York: W. H. Freeman, 2007):

A hospital study that compared brain cancer patients and a similar group without brain cancer found no statistically significant association between cell phone use and a group of brain cancers known as gliomas. But when 20 types of glioma were considered separately, an association was found between cell phone use and one rare form. Puzzlingly, however, this risk appeared to decrease rather than increase with greater mobile phone use.

This is an example of a probable type I error. Suppose we conducted 20 hypotheses tests with the null hypothesis “Cell phone use is not associated with cancer” at the 5% level. We expect 1 in 20 (5%) to give significant results by chance alone when there is no association between cell phone use and cancer. So the conclusion that this one type of cancer is related to cell phone use is probably just a result of random chance and not an indication of an association.

Click here to see a fun cartoon that illustrates this same idea.

How Many People Are Telepathic?

Telepathy is the ability to read minds. Researchers used Zener cards in the early 1900s for experimental research into telepathy.

5 Zener cards. The first has a circle, the second a +, the third three wavy lines, the fourth a square, and the fifth a star.

In a telepathy experiment, the “sender” looks at 1 of 5 Zener cards while the “receiver” guesses the symbol. This is repeated 40 times, and the proportion of correct responses is recorded. Because there are 5 cards, we expect random guesses to be right 20% of the time (1 out of 5) in the long run. So in 40 tries, 8 correct guesses, a proportion of 0.20, is common. But of course there will be variability even when someone is just guessing. Thirteen or more correct in 40 tries, a proportion of 0.325, is statistically significant at the 5% level. When people perform this well on the telepathy test, we conclude their performance is not due to chance and take it as an indication of the ability to read minds.

In the next section, “Hypothesis Test for a Population Proportion,” we learn the details of hypothesis testing for claims about a population proportion. Before we get into the details, we want to step back and think more generally about hypothesis testing. We close our introduction to hypothesis testing with a helpful analogy.

Courtroom Analogy for Hypothesis Tests

When a defendant stands trial for a crime, he or she is innocent until proven guilty. It is the job of the prosecution to present evidence showing that the defendant is guilty beyond a reasonable doubt . It is the job of the defense to challenge this evidence to establish a reasonable doubt. The jury weighs the evidence and makes a decision.

When a jury makes a decision, it has only two possible verdicts:

Guilty: The jury concludes that there is enough evidence to convict the defendant. The evidence is so strong that there is not a reasonable doubt that the defendant is guilty.
Not Guilty: The jury concludes that there is not enough evidence to conclude beyond a reasonable doubt that the person is guilty. Notice that they do not conclude that the person is innocent. This verdict says only that there is not enough evidence to return a guilty verdict.

How is this example like a hypothesis test?

The null hypothesis is “The person is innocent.” The alternative hypothesis is “The person is guilty.” The evidence is the data. In a courtroom, the person is assumed innocent until proven guilty. In a hypothesis test, we assume the null hypothesis is true until the data proves otherwise.

The two possible verdicts are similar to the two conclusions that are possible in a hypothesis test.

Reject the null hypothesis: When we reject a null hypothesis, we accept the alternative hypothesis. This is like a guilty verdict. The evidence is strong enough for the jury to reject the assumption of innocence. In a hypothesis test, the data is strong enough for us to reject the assumption that the null hypothesis is true.

Fail to reject the null hypothesis: When we fail to reject the null hypothesis, we are delivering a “not guilty” verdict. The jury concludes that the evidence is not strong enough to reject the assumption of innocence, so the evidence is too weak to support a guilty verdict. We conclude the data is not strong enough to reject the null hypothesis, so the data is too weak to accept the alternative hypothesis.

How does the courtroom analogy relate to type I and type II errors?

Type I error: The jury convicts an innocent person. By analogy, we reject a true null hypothesis and accept a false alternative hypothesis.

Type II error: The jury says a person is not guilty when he or she really is. By analogy, we fail to reject a null hypothesis that is false. In other words, we do not accept an alternative hypothesis when it is really true.

Let’s Summarize

In this section, we introduced the four-step process of hypothesis testing:

Step 1: Determine the hypotheses.

The hypotheses are claims about the population(s).
The null hypothesis is a hypothesis that the parameter equals a specific value.
The alternative hypothesis is the competing claim that the parameter is less than, greater than, or not equal to the parameter value in the null. The claim that drives the statistical investigation is usually found in the alternative hypothesis.

Step 2: Collect the data.

Because the hypothesis test is based on probability, random selection or assignment is essential in data production.

Step 3: Assess the evidence.

Use the data to find a P-value.
The P-value is a probability statement about how unlikely the data is if the null hypothesis is true.
More specifically, the P-value gives the probability of sample results at least as extreme as the data if the null hypothesis is true.

Step 4: Give the conclusion.

A small P-value says the data is unlikely to occur if the null hypothesis is true. We therefore conclude that the null hypothesis is probably not true and that the alternative hypothesis is true instead.
We often choose a significance level as a benchmark for judging if the P-value is small enough. If the P-value is less than or equal to the significance level, we reject the null hypothesis and accept the alternative hypothesis instead.
If the P-value is greater than the significance level, we say we “fail to reject” the null hypothesis. We never say that we “accept” the null hypothesis. We just say that we don’t have enough evidence to reject it. This is equivalent to saying we don’t have enough evidence to support the alternative hypothesis.
Our conclusion will respond to the research question, so we often state the conclusion in terms of the alternative hypothesis.

Inference is based on probability, so there is always uncertainty. Although we may have strong evidence against it, the null hypothesis may still be true. If this is the case, we have a type I error. Similarly, even if we fail to reject the null hypothesis, it does not mean the alternative hypothesis is false. In this case, we have a type II error. These errors are not the result of a mistake in conducting the hypothesis test. They occur because of random chance.

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9.5: Additional Information and Full Hypothesis Test Examples

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In a hypothesis test problem, you may see words such as "the level of significance is 1%." The "1%" is the preconceived or preset $\alpha$.
The statistician setting up the hypothesis test selects the value of α to use before collecting the sample data.
If no level of significance is given, a common standard to use is $\alpha = 0.05$.
When you calculate the $p$-value and draw the picture, the $p$-value is the area in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two tailed.
The alternative hypothesis, $H_{a}$, tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test.
$H_{a}$ never has a symbol that contains an equal sign.
Thinking about the meaning of the $p$-value: A data analyst (and anyone else) should have more confidence that he made the correct decision to reject the null hypothesis with a smaller $p$-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha. Similarly, for a large p -value such as 0.4, as opposed to a $p$-value of 0.056 ($\alpha = 0.05$ is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis. This makes the data analyst use judgment rather than mindlessly applying rules.

The following examples illustrate a left-, right-, and two-tailed test.

Example $\PageIndex{1}$

$H_{0}: \mu = 5, H_{a}: \mu < 5$

Test of a single population mean. $H_{a}$ tells you the test is left-tailed. The picture of the $p$-value is as follows:

Normal distribution curve of a single population mean with a value of 5 on the x-axis and the p-value points to the area on the left tail of the curve.

Exercise $\PageIndex{1}$

$H_{0}: \mu = 10, H_{a}: \mu < 10$

Assume the $p$-value is 0.0935. What type of test is this? Draw the picture of the $p$-value.

left-tailed test

Example $\PageIndex{2}$

$H_{0}: \mu \leq 0.2, H_{a}: \mu > 0.2$

This is a test of a single population proportion. $H_{a}$ tells you the test is right-tailed . The picture of the p -value is as follows:

Normal distribution curve of a single population proportion with the value of 0.2 on the x-axis. The p-value points to the area on the right tail of the curve.

Exercise $\PageIndex{2}$

$H_{0}: \mu \leq 1, H_{a}: \mu > 1$

Assume the $p$-value is 0.1243. What type of test is this? Draw the picture of the $p$-value.

right-tailed test

Example $\PageIndex{3}$

$H_{0}: \mu = 50, H_{a}: \mu \neq 50$

This is a test of a single population mean. $H_{a}$ tells you the test is two-tailed . The picture of the $p$-value is as follows.

Normal distribution curve of a single population mean with a value of 50 on the x-axis. The p-value formulas, 1/2(p-value), for a two-tailed test is shown for the areas on the left and right tails of the curve.

Exercise $\PageIndex{3}$

$H_{0}: \mu = 0.5, H_{a}: \mu \neq 0.5$

Assume the p -value is 0.2564. What type of test is this? Draw the picture of the $p$-value.

two-tailed test

Full Hypothesis Test Examples

Example $\pageindex{4}$.

Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds . His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims . For the 15 swims, Jeffrey's mean time was 16 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a preset α = 0.05. Assume that the swim times for the 25-yard freestyle are normal.

Set up the Hypothesis Test:

Since the problem is about a mean, this is a test of a single population mean .

$H_{0}: \mu = 16.43, H_{a}: \mu < 16.43$

For Jeffrey to swim faster, his time will be less than 16.43 seconds. The "$<$" tells you this is left-tailed.

Determine the distribution needed:

Random variable: $\bar{X} =$ the mean time to swim the 25-yard freestyle.

Distribution for the test: $\bar{X}$ is normal (population standard deviation is known: $\sigma = 0.8$)

$\bar{X} - N \left(\mu, \frac{\sigma_{x}}{\sqrt{n}}\right)$ Therefore, $\bar{X} - N\left(16.43, \frac{0.8}{\sqrt{15}}\right)$

$\mu = 16.43$ comes from $H_{0}$ and not the data. $\sigma = 0.8$, and $n = 15$.

Calculate the $p-\text{value}$ using the normal distribution for a mean:

$p\text{-value} = P(\bar{x} < 16) = 0.0187$ where the sample mean in the problem is given as 16.

$p\text{-value} = 0.0187$ (This is called the actual level of significance .) The $p-\text{value}$ is the area to the left of the sample mean is given as 16.

Normal distribution curve for the average time to swim the 25-yard freestyle with values 16, as the sample mean, and 16.43 on the x-axis. A vertical upward line extends from 16 on the x-axis to the curve. An arrow points to the left tail of the curve.

$\mu = 16.43$ comes from $H_{0}$. Our assumption is $\mu = 16.43$.

Interpretation of the $p-\text{value}$: If $H_{0}$ is true , there is a 0.0187 probability (1.87%) that Jeffrey's mean time to swim the 25-yard freestyle is 16 seconds or less. Because a 1.87% chance is small, the mean time of 16 seconds or less is unlikely to have happened randomly. It is a rare event.

Compare $\alpha$ and the $p-\text{value}$:

$\alpha = 0.05 p\text{-value} = 0.0187 \alpha > p\text{-value}$

Make a decision: Since $\alpha > p\text{-value}$, reject $H_{0}$.

This means that you reject $\mu = 16.43$. In other words, you do not think Jeffrey swims the 25-yard freestyle in 16.43 seconds but faster with the new goggles.

Conclusion: At the 5% significance level, we conclude that Jeffrey swims faster using the new goggles. The sample data show there is sufficient evidence that Jeffrey's mean time to swim the 25-yard freestyle is less than 16.43 seconds.

The p -value can easily be calculated.

Press STAT and arrow over to TESTS . Press 1:Z-Test . Arrow over to Stats and press ENTER . Arrow down and enter 16.43 for $\mu_{0}$ (null hypothesis), .8 for σ , 16 for the sample mean, and 15 for n . Arrow down to $\mu$ : (alternate hypothesis) and arrow over to $< \mu_{0}$. Press ENTER . Arrow down to Calculate and press ENTER . The calculator not only calculates the p -value ($p = 0.0187$) but it also calculates the test statistic ( z -score) for the sample mean. $\mu < 16.43$ is the alternative hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with $z = -2.08$ (test statistic) and $p = 0.0187$ ($p-\text{value}$). Make sure when you use Draw that no other equations are highlighted in $Y =$ and the plots are turned off.

When the calculator does a $Z$-Test, the Z-Test function finds the p -value by doing a normal probability calculation using the central limit theorem:

$P(\bar{X} < 16)$ 2nd DISTR normcdf ($(−10^{99},16,16.43,\frac{0.8}{\sqrt{15}})$.

The Type I and Type II errors for this problem are as follows:

The Type I error is to conclude that Jeffrey swims the 25-yard freestyle, on average, in less than 16.43 seconds when, in fact, he actually swims the 25-yard freestyle, on average, in 16.43 seconds. (Reject the null hypothesis when the null hypothesis is true.)

The Type II error is that there is not evidence to conclude that Jeffrey swims the 25-yard free-style, on average, in less than 16.43 seconds when, in fact, he actually does swim the 25-yard free-style, on average, in less than 16.43 seconds. (Do not reject the null hypothesis when the null hypothesis is false.)

Exercise $\PageIndex{4}$

The mean throwing distance of a football for a Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset $\alpha = 0.05$. Assume the throw distances for footballs are normal.

First, determine what type of test this is, set up the hypothesis test, find the p -value, sketch the graph, and state your conclusion.

Press STAT and arrow over to TESTS. Press 1: $Z$-Test. Arrow over to Stats and press ENTER. Arrow down and enter 40 for $\mu_{0}$ (null hypothesis), 2 for $\sigma$, 45 for the sample mean, and 20 for $n$. Arrow down to $\mu$: (alternative hypothesis) and set it either as $<$, $\neq$, or $>$. Press ENTER. Arrow down to Calculate and press ENTER. The calculator not only calculates the p -value but it also calculates the test statistic ( z -score) for the sample mean. Select $<$, $\neq$, or $>$ for the alternative hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate). Press ENTER. A shaded graph appears with test statistic and $p$-value. Make sure when you use Draw that no other equations are highlighted in $Y =$ and the plots are turned off.

Since the problem is about a mean, this is a test of a single population mean.

$H_{0}: \mu = 40$
$H_{a}: \mu > 40$
$p = 0.0062$

Because $p < \alpha$, we reject the null hypothesis. There is sufficient evidence to suggest that the change in grip improved Marco’s throwing distance.

Historical Note

The traditional way to compare the two probabilities, $\alpha$ and the $p-\text{value}$, is to compare the critical value ($z$-score from $\alpha$) to the test statistic ($z$-score from data). The calculated test statistic for the $p$-value is –2.08. (From the Central Limit Theorem, the test statistic formula is $z = \frac{\bar{x}-\mu_{x}}{\left(\frac{\sigma_{x}}{\sqrt{n}}\right)}$. For this problem, $\bar{x} = 16$, $\mu_{x} = 16.43$ from the null hypotheses is, $\sigma_{x} = 0.8$, and $n = 15$.) You can find the critical value for $\alpha = 0.05$ in the normal table (see 15.Tables in the Table of Contents). The $z$-score for an area to the left equal to 0.05 is midway between –1.65 and –1.64 (0.05 is midway between 0.0505 and 0.0495). The $z$-score is –1.645. Since –1.645 > –2.08 (which demonstrates that $\alpha > p-\text{value}$), reject $H_{0}$. Traditionally, the decision to reject or not reject was done in this way. Today, comparing the two probabilities $\alpha$ and the $p$-value is very common. For this problem, the $p-\text{value}$, 0.0187 is considerably smaller than $\alpha = 0.05$. You can be confident about your decision to reject. The graph shows $\alpha$, the $p-\text{value}$, and the test statistics and the critical value.

Distribution curve comparing the α to the p-value. Values of -2.15 and -1.645 are on the x-axis. Vertical upward lines extend from both of these values to the curve. The p-value is equal to 0.0158 and points to the area to the left of -2.15. α is equal to 0.05 and points to the area between the values of -2.15 and -1.645.

Example $\PageIndex{5}$

A college football coach thought that his players could bench press a mean weight of 275 pounds . It is known that the standard deviation is 55 pounds . Three of his players thought that the mean weight was more than that amount. They asked 30 of their teammates for their estimated maximum lift on the bench press exercise. The data ranged from 205 pounds to 385 pounds. The actual different weights were (frequencies are in parentheses) 205(3); 215(3); 225(1); 241(2); 252(2); 265(2); 275(2); 313(2); 316(5); 338(2); 341(1); 345(2); 368(2); 385(1).

Conduct a hypothesis test using a 2.5% level of significance to determine if the bench press mean is more than 275 pounds.

Since the problem is about a mean weight, this is a test of a single population mean.

$H_{0}: \mu = 275$
$H_{a}: \mu > 275$

This is a right-tailed test.

Calculating the distribution needed:

Random variable: $\bar{X} =$ the mean weight, in pounds, lifted by the football players.

Distribution for the test: It is normal because $\sigma$ is known.

$\bar{X} - N\left(275, \frac{55}{\sqrt{30}}\right)$
$\bar{x} = 286.2$ pounds (from the data).
$\sigma = 55$ pounds (Always use $\sigma$ if you know it.) We assume $\mu = 275$ pounds unless our data shows us otherwise.

Calculate the p -value using the normal distribution for a mean and using the sample mean as input (see [link] for using the data as input):

\[p\text{-value} = P(\bar{x} > 286.2) = 0.1323.\nonumber \]

Interpretation of the p -value: If $H_{0}$ is true, then there is a 0.1331 probability (13.23%) that the football players can lift a mean weight of 286.2 pounds or more. Because a 13.23% chance is large enough, a mean weight lift of 286.2 pounds or more is not a rare event.

Normal distribution curve of the average weight lifted by football players with values of 275 and 286.2 on the x-axis. A vertical upward line extends from 286.2 to the curve. The p-value points to the area to the right of 286.2.

$\alpha = 0.025 p-value = 0.1323$

Make a decision: Since $\alpha < p\text{-value}$, do not reject $H_{0}$.

Conclusion: At the 2.5% level of significance, from the sample data, there is not sufficient evidence to conclude that the true mean weight lifted is more than 275 pounds.

The $p-\text{value}$ can easily be calculated.

Put the data and frequencies into lists. Press STAT and arrow over to TESTS . Press 1:Z-Test . Arrow over to Data and press ENTER . Arrow down and enter 275 for $\mu_{0}$, 55 for $\sigma$, the name of the list where you put the data, and the name of the list where you put the frequencies. Arrow down to $\mu$ : and arrow over to $> \mu_{0}$. Press ENTER . Arrow down to Calculate and press ENTER . The calculator not only calculates the $p-\text{value}$ ($p = 0.1331$), a little different from the previous calculation - in it we used the sample mean rounded to one decimal place instead of the data) but it also calculates the test statistic ( z -score) for the sample mean, the sample mean, and the sample standard deviation. $\mu > 275$ is the alternative hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with $z = 1.112$ (test statistic) and $p = 0.1331$ ($p-\text{value})$. Make sure when you use Draw that no other equations are highlighted in $Y =$ and the plots are turned off.

Example $\PageIndex{6}$

Statistics students believe that the mean score on the first statistics test is 65. A statistics instructor thinks the mean score is higher than 65. He samples ten statistics students and obtains the scores 65 65 70 67 66 63 63 68 72 71. He performs a hypothesis test using a 5% level of significance. The data are assumed to be from a normal distribution.

Set up the hypothesis test:

A 5% level of significance means that $\alpha = 0.05$. This is a test of a single population mean .

$H_{0}: \mu = 65 H_{a}: \mu > 65$

Since the instructor thinks the average score is higher, use a "$>$". The "$>$" means the test is right-tailed.

Random variable: $\bar{X} =$ average score on the first statistics test.

Distribution for the test: If you read the problem carefully, you will notice that there is no population standard deviation given . You are only given $n = 10$ sample data values. Notice also that the data come from a normal distribution. This means that the distribution for the test is a student's $t$.

Use $t_{df}$. Therefore, the distribution for the test is $t_{9}$ where $n = 10$ and $df = 10 - 1 = 9$.

Calculate the $p$-value using the Student's $t$-distribution:

$p\text{-value} = P(\bar{x} > 67) = 0.0396$ where the sample mean and sample standard deviation are calculated as 67 and 3.1972 from the data.

Interpretation of the p -value: If the null hypothesis is true, then there is a 0.0396 probability (3.96%) that the sample mean is 65 or more.

Normal distribution curve of average scores on the first statistic tests with 65 and 67 values on the x-axis. A vertical upward line extends from 67 to the curve. The p-value points to the area to the right of 67.

Since $α = 0.05$ and $p\text{-value} = 0.0396$. $\alpha > p\text{-value}$.

This means you reject $\mu = 65$. In other words, you believe the average test score is more than 65.

Conclusion: At a 5% level of significance, the sample data show sufficient evidence that the mean (average) test score is more than 65, just as the math instructor thinks.

The $p\text{-value}$ can easily be calculated.

Put the data into a list. Press STAT and arrow over to TESTS . Press 2:T-Test . Arrow over to Data and press ENTER . Arrow down and enter 65 for $\mu_{0}$, the name of the list where you put the data, and 1 for Freq: . Arrow down to $\mu$: and arrow over to $> \mu_{0}$. Press ENTER . Arrow down to Calculate and press ENTER . The calculator not only calculates the $p\text{-value}$ (p = 0.0396) but it also calculates the test statistic ( t -score) for the sample mean, the sample mean, and the sample standard deviation. $\mu > 65$ is the alternative hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with $t = 1.9781$ (test statistic) and $p = 0.0396$ ($p\text{-value}$). Make sure when you use Draw that no other equations are highlighted in $Y =$ and the plots are turned off.

Exercise $\PageIndex{6}$

It is believed that a stock price for a particular company will grow at a rate of $5 per week with a standard deviation of $1. An investor believes the stock won’t grow as quickly. The changes in stock price is recorded for ten weeks and are as follows: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. Perform a hypothesis test using a 5% level of significance. State the null and alternative hypotheses, find the p -value, state your conclusion, and identify the Type I and Type II errors.

$H_{0}: \mu = 5$
$H_{a}: \mu < 5$
$p = 0.0082$

Because $p < \alpha$, we reject the null hypothesis. There is sufficient evidence to suggest that the stock price of the company grows at a rate less than $5 a week.

Type I Error: To conclude that the stock price is growing slower than $5 a week when, in fact, the stock price is growing at $5 a week (reject the null hypothesis when the null hypothesis is true).
Type II Error: To conclude that the stock price is growing at a rate of $5 a week when, in fact, the stock price is growing slower than $5 a week (do not reject the null hypothesis when the null hypothesis is false).

Example $\PageIndex{7}$

Joon believes that 50% of first-time brides in the United States are younger than their grooms. She performs a hypothesis test to determine if the percentage is the same or different from 50% . Joon samples 100 first-time brides and 53 reply that they are younger than their grooms. For the hypothesis test, she uses a 1% level of significance.

The 1% level of significance means that α = 0.01. This is a test of a single population proportion .

$H_{0}: p = 0.50$ $H_{a}: p \neq 0.50$

The words "is the same or different from" tell you this is a two-tailed test.

Calculate the distribution needed:

Random variable: $P′ =$ the percent of of first-time brides who are younger than their grooms.

Distribution for the test: The problem contains no mention of a mean. The information is given in terms of percentages. Use the distribution for P′ , the estimated proportion.

\[P' - N\left(p, \sqrt{\frac{p-q}{n}}\right)\nonumber \]

\[P' - N\left(0.5, \sqrt{\frac{0.5-0.5}{100}}\right)\nonumber \]

where $p = 0.50, q = 1−p = 0.50$, and $n = 100$

Calculate the p -value using the normal distribution for proportions:

\[p\text{-value} = P(p′ < 0.47 \space or \space p′ > 0.53) = 0.5485\nonumber \]

where \[x = 53, p' = \frac{x}{n} = \frac{53}{100} = 0.53\nonumber \].

Interpretation of the p-value: If the null hypothesis is true, there is 0.5485 probability (54.85%) that the sample (estimated) proportion $p'$ is 0.53 or more OR 0.47 or less (see the graph in Figure).

Normal distribution curve of the percent of first time brides who are younger than the groom with values of 0.47, 0.50, and 0.53 on the x-axis. Vertical upward lines extend from 0.47 and 0.53 to the curve. 1/2(p-values) are calculated for the areas on outsides of 0.47 and 0.53.

$\mu = p = 0.50$ comes from $H_{0}$, the null hypothesis.

$p′ = 0.53$. Since the curve is symmetrical and the test is two-tailed, the $p′$ for the left tail is equal to $0.50 – 0.03 = 0.47$ where $\mu = p = 0.50$. (0.03 is the difference between 0.53 and 0.50.)

Compare $\alpha$ and the $p\text{-value}$:

Since $\alpha = 0.01$ and $p\text{-value} = 0.5485$. $\alpha < p\text{-value}$.

Make a decision: Since $\alpha < p\text{-value}$, you cannot reject $H_{0}$.

Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of first-time brides who are younger than their grooms is different from 50%.

Press STAT and arrow over to TESTS . Press 5:1-PropZTest . Enter .5 for $p_{0}$, 53 for $x$ and 100 for $n$. Arrow down to Prop and arrow to not equals $p_{0}$. Press ENTER . Arrow down to Calculate and press ENTER . The calculator calculates the $p\text{-value}$ ($p = 0.5485$) and the test statistic ($z$-score). Prop not equals .5 is the alternate hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with $z = 0.6$ (test statistic) and $p = 0.5485$ ($p\text{-value}$). Make sure when you use Draw that no other equations are highlighted in $Y =$ and the plots are turned off.

The Type I and Type II errors are as follows:

The Type I error is to conclude that the proportion of first-time brides who are younger than their grooms is different from 50% when, in fact, the proportion is actually 50%. (Reject the null hypothesis when the null hypothesis is true).

The Type II error is there is not enough evidence to conclude that the proportion of first time brides who are younger than their grooms differs from 50% when, in fact, the proportion does differ from 50%. (Do not reject the null hypothesis when the null hypothesis is false.)

Exercise $\PageIndex{7}$

A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.

First, determine what type of test this is, set up the hypothesis test, find the $p\text{-value}$, sketch the graph, and state your conclusion.

Since the problem is about percentages, this is a test of single population proportions.

$H_{0} : p = 0.85$
$H_{a}: p \neq 0.85$
$p = 0.7554$

Because $p > \alpha$, we fail to reject the null hypothesis. There is not sufficient evidence to suggest that the proportion of students that want to go to the zoo is not 85%.

Example $\PageIndex{8}$

Suppose a consumer group suspects that the proportion of households that have three cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

$H_{0}: p = 0.30, H_{a}: p \neq 0.30$

The random variable is $P′ =$ proportion of households that have three cell phones.

The distribution for the hypothesis test is $P' - N\left(0.30, \sqrt{\frac{(0.30 \cdot 0.70)}{150}}\right)$

Exercise $\PageIndex{8}$.2

a. The value that helps determine the $p\text{-value}$ is $p′$. Calculate $p′$.

a. $p' = \frac{x}{n}$ where $x$ is the number of successes and $n$ is the total number in the sample.

$x = 43, n = 150$

$p′ = 43150$

Exercise $\PageIndex{8}$.3

b. What is a success for this problem?

b. A success is having three cell phones in a household.

Exercise $\PageIndex{8}$.4

c. What is the level of significance?

c. The level of significance is the preset $\alpha$. Since $\alpha$ is not given, assume that $\alpha = 0.05$.

Exercise $\PageIndex{8}$.5

d. Draw the graph for this problem. Draw the horizontal axis. Label and shade appropriately.

Calculate the $p\text{-value}$.

d. $p\text{-value} = 0.7216$

Exercise $\PageIndex{8}$.6

e. Make a decision. _____________(Reject/Do not reject) $H_{0}$ because____________.

e. Assuming that $\alpha = 0.05, \alpha < p\text{-value}$. The decision is do not reject $H_{0}$ because there is not sufficient evidence to conclude that the proportion of households that have three cell phones is not 30%.

Exercise $\PageIndex{8}$

Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 5% level of significance. State the null and alternative hypothesis, find the p -value, state your conclusion, and identify the Type I and Type II errors.

$H_{0}: p = 0.92$
$H_{a}: p < 0.92$
$p\text{-value} = 0.0046$

Because $p < 0.05$, we reject the null hypothesis. There is sufficient evidence to conclude that fewer than 92% of American adults own cell phones.

Type I Error: To conclude that fewer than 92% of American adults own cell phones when, in fact, 92% of American adults do own cell phones (reject the null hypothesis when the null hypothesis is true).
Type II Error: To conclude that 92% of American adults own cell phones when, in fact, fewer than 92% of American adults own cell phones (do not reject the null hypothesis when the null hypothesis is false).

The next example is a poem written by a statistics student named Nicole Hart. The solution to the problem follows the poem. Notice that the hypothesis test is for a single population proportion. This means that the null and alternate hypotheses use the parameter $p$. The distribution for the test is normal. The estimated proportion $p′$ is the proportion of fleas killed to the total fleas found on Fido. This is sample information. The problem gives a preconceived $\alpha = 0.01$, for comparison, and a 95% confidence interval computation. The poem is clever and humorous, so please enjoy it!

Example $\PageIndex{9}$

My dog has so many fleas,

They do not come off with ease. As for shampoo, I have tried many types Even one called Bubble Hype, Which only killed 25% of the fleas, Unfortunately I was not pleased.

I've used all kinds of soap, Until I had given up hope Until one day I saw An ad that put me in awe.

A shampoo used for dogs Called GOOD ENOUGH to Clean a Hog Guaranteed to kill more fleas.

I gave Fido a bath And after doing the math His number of fleas Started dropping by 3's! Before his shampoo I counted 42.

At the end of his bath, I redid the math And the new shampoo had killed 17 fleas. So now I was pleased.

Now it is time for you to have some fun With the level of significance being .01, You must help me figure out

Use the new shampoo or go without?

$H_{0}: p \leq 0.25$ $H_{a}: p > 0.25$

In words, CLEARLY state what your random variable $\bar{X}$ or $P′$ represents.

$P′ =$ The proportion of fleas that are killed by the new shampoo

State the distribution to use for the test.

\[N\left(0.25, \sqrt{\frac{(0.25){1-0.25}}{42}}\right)\nonumber \]

Test Statistic: $z = 2.3163$

Calculate the $p\text{-value}$ using the normal distribution for proportions:

\[p\text{-value} = 0.0103\nonumber \]

In one to two complete sentences, explain what the p -value means for this problem.

If the null hypothesis is true (the proportion is 0.25), then there is a 0.0103 probability that the sample (estimated) proportion is 0.4048 $\left(\frac{17}{42}\right)$ or more.

Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the $p\text{-value}$.

Normal distribution graph of the proportion of fleas killed by the new shampoo with values of 0.25 and 0.4048 on the x-axis. A vertical upward line extends from 0.4048 to the curve and the area to the left of this is shaded in. The test statistic of the sample proportion is listed.

Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of fleas that are killed by the new shampoo is more than 25%.

Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

Normal distribution graph of the proportion of fleas killed by the new shampoo with values of 0.26, 17/42, and 0.55 on the x-axis. A vertical upward line extends from 0.26 and 0.55. The area between these two points is equal to 0.95.

Confidence Interval: (0.26,0.55) We are 95% confident that the true population proportion p of fleas that are killed by the new shampoo is between 26% and 55%.

This test result is not very definitive since the $p\text{-value}$ is very close to alpha. In reality, one would probably do more tests by giving the dog another bath after the fleas have had a chance to return.

Example $\PageIndex{10}$

The National Institute of Standards and Technology provides exact data on conductivity properties of materials. Following are conductivity measurements for 11 randomly selected pieces of a particular type of glass.

1.11; 1.07; 1.11; 1.07; 1.12; 1.08; .98; .98 1.02; .95; .95

Is there convincing evidence that the average conductivity of this type of glass is greater than one? Use a significance level of 0.05. Assume the population is normal.

Let’s follow a four-step process to answer this statistical question.

$H_{0}: \mu \leq 1$
$H_{a}: \mu > 1$
Plan : We are testing a sample mean without a known population standard deviation. Therefore, we need to use a Student's-t distribution. Assume the underlying population is normal.
Do the calculations : We will input the sample data into the TI-83 as follows.

4. State the Conclusions : Since the $p\text{-value} (p = 0.036)$ is less than our alpha value, we will reject the null hypothesis. It is reasonable to state that the data supports the claim that the average conductivity level is greater than one.

Example $\PageIndex{11}$

In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue, use a 0.005 significance level. Explain why the significance level should be so low in terms of a Type I error.

We will follow the four-step process.

$H_{0}: p \leq 0.00034$
$H_{a}: p > 0.00034$

If we commit a Type I error, we are essentially accepting a false claim. Since the claim describes cancer-causing environments, we want to minimize the chances of incorrectly identifying causes of cancer.

We will be testing a sample proportion with $x = 172$ and $n = 420,019$. The sample is sufficiently large because we have $np = 420,019(0.00034) = 142.8$, $nq = 420,019(0.99966) = 419,876.2$, two independent outcomes, and a fixed probability of success $p = 0.00034$. Thus we will be able to generalize our results to the population.

Figure $\PageIndex{11}$.

Figure $\PageIndex{12}$.

Since the $p\text{-value} = 0.0073$ is greater than our alpha value $= 0.005$, we cannot reject the null. Therefore, we conclude that there is not enough evidence to support the claim of higher brain cancer rates for the cell phone users.

Example $\PageIndex{12}$

According to the US Census there are approximately 268,608,618 residents aged 12 and older. Statistics from the Rape, Abuse, and Incest National Network indicate that, on average, 207,754 rapes occur each year (male and female) for persons aged 12 and older. This translates into a percentage of sexual assaults of 0.078%. In Daviess County, KY, there were reported 11 rapes for a population of 37,937. Conduct an appropriate hypothesis test to determine if there is a statistically significant difference between the local sexual assault percentage and the national sexual assault percentage. Use a significance level of 0.01.

We will follow the four-step plan.

We need to test whether the proportion of sexual assaults in Daviess County, KY is significantly different from the national average.
$H_{0}: p = 0.00078$
$H_{a}: p \neq 0.00078$

Figure $\PageIndex{13}$.

Figure $\PageIndex{14}$.

Since the $p\text{-value}$, $p = 0.00063$, is less than the alpha level of 0.01, the sample data indicates that we should reject the null hypothesis. In conclusion, the sample data support the claim that the proportion of sexual assaults in Daviess County, Kentucky is different from the national average proportion.

The hypothesis test itself has an established process. This can be summarized as follows:

Determine $H_{0}$ and $H_{a}$. Remember, they are contradictory.
Determine the random variable.
Determine the distribution for the test.
Draw a graph, calculate the test statistic, and use the test statistic to calculate the $p\text{-value}$. (A z -score and a t -score are examples of test statistics.)
Compare the preconceived α with the p -value, make a decision (reject or do not reject H 0 ), and write a clear conclusion using English sentences.

Notice that in performing the hypothesis test, you use $\alpha$ and not $\beta$. $\beta$ is needed to help determine the sample size of the data that is used in calculating the $p\text{-value}$. Remember that the quantity $1 – \beta$ is called the Power of the Test . A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same.If the power is low, the null hypothesis might not be rejected when it should be.

Assume $H_{0}: \mu = 9$ and $H_{a}: \mu < 9$. Is this a left-tailed, right-tailed, or two-tailed test?

This is a left-tailed test.

Exercise $\PageIndex{9}$

Assume $H_{0}: \mu \leq 6$ and $H_{a}: \mu > 6$. Is this a left-tailed, right-tailed, or two-tailed test?

Exercise $\PageIndex{10}$

Assume $H_{0}: p = 0.25$ and $H_{a}: p \neq 0.25$. Is this a left-tailed, right-tailed, or two-tailed test?

This is a two-tailed test.

Exercise $\PageIndex{11}$

Draw the general graph of a left-tailed test.

Exercise $\PageIndex{12}$

Draw the graph of a two-tailed test.

Exercise $\PageIndex{13}$

A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use?

Exercise $\PageIndex{14}$

Your friend claims that his mean golf score is 63. You want to show that it is higher than that. What type of test would you use?

a right-tailed test

Exercise $\PageIndex{15}$

A bathroom scale claims to be able to identify correctly any weight within a pound. You think that it cannot be that accurate. What type of test would you use?

Exercise $\PageIndex{16}$

You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you think it is less for this particular coin. What type of test would you use?

a left-tailed test

Exercise $\PageIndex{17}$

If the alternative hypothesis has a not equals ( $\neq$ ) symbol, you know to use which type of test?

Exercise $\PageIndex{18}$

Assume the null hypothesis states that the mean is at least 18. Is this a left-tailed, right-tailed, or two-tailed test?

Exercise $\PageIndex{19}$

Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?

Exercise $\PageIndex{20}$

Assume the null hypothesis states that the mean is equal to 88. The alternative hypothesis states that the mean is not equal to 88. Is this a left-tailed, right-tailed, or two-tailed test?

Data from Amit Schitai. Director of Instructional Technology and Distance Learning. LBCC.
Data from Bloomberg Businessweek . Available online at www.businessweek.com/news/2011- 09-15/nyc-smoking-rate-falls-to-record-low-of-14-bloomberg-says.html.
Data from energy.gov. Available online at http://energy.gov (accessed June 27. 2013).
Data from Gallup®. Available online at www.gallup.com (accessed June 27, 2013).
Data from Growing by Degrees by Allen and Seaman.
Data from La Leche League International. Available online at www.lalecheleague.org/Law/BAFeb01.html.
Data from the American Automobile Association. Available online at www.aaa.com (accessed June 27, 2013).
Data from the American Library Association. Available online at www.ala.org (accessed June 27, 2013).
Data from the Bureau of Labor Statistics. Available online at http://www.bls.gov/oes/current/oes291111.htm .
Data from the Centers for Disease Control and Prevention. Available online at www.cdc.gov (accessed June 27, 2013)
Data from the U.S. Census Bureau, available online at quickfacts.census.gov/qfd/states/00000.html (accessed June 27, 2013).
Data from the United States Census Bureau. Available online at www.census.gov/hhes/socdemo/language/.
Data from Toastmasters International. Available online at http://toastmasters.org/artisan/deta...eID=429&Page=1 .
Data from Weather Underground. Available online at www.wunderground.com (accessed June 27, 2013).
Federal Bureau of Investigations. “Uniform Crime Reports and Index of Crime in Daviess in the State of Kentucky enforced by Daviess County from 1985 to 2005.” Available online at http://www.disastercenter.com/kentucky/crime/3868.htm (accessed June 27, 2013).
“Foothill-De Anza Community College District.” De Anza College, Winter 2006. Available online at research.fhda.edu/factbook/DA...t_da_2006w.pdf.
Johansen, C., J. Boice, Jr., J. McLaughlin, J. Olsen. “Cellular Telephones and Cancer—a Nationwide Cohort Study in Denmark.” Institute of Cancer Epidemiology and the Danish Cancer Society, 93(3):203-7. Available online at http://www.ncbi.nlm.nih.gov/pubmed/11158188 (accessed June 27, 2013).
Rape, Abuse & Incest National Network. “How often does sexual assault occur?” RAINN, 2009. Available online at www.rainn.org/get-information...sexual-assault (accessed June 27, 2013).

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What is the difference between a hypothesis and a conclusion?

And a conclusion is drawn AFTER the experiment is performed, and reports whether or not the results of the experiment supported the original hypothesis...

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How to Write Hypothesis Test Conclusions (With Examples)
Example 1: Reject the Null Hypothesis Conclusion. Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month. She then performs a hypothesis test ...
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4. Refine your hypothesis. You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain: The relevant variables; The specific group being studied; The predicted outcome of the experiment or analysis; 5.
How to Write a Hypothesis in 6 Steps, With Examples
4 Alternative hypothesis. An alternative hypothesis, abbreviated as H 1 or H A, is used in conjunction with a null hypothesis. It states the opposite of the null hypothesis, so that one and only one must be true. Examples: Plants grow better with bottled water than tap water. Professional psychics win the lottery more than other people. 5 ...
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A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.. To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:. Null Hypothesis (H 0): The sample data occurs purely from chance.
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For example, a hypothesis like "Sunflower plants need water to grow" is not falsifiable, as it is already a well-established fact. But a hypothesis regarding frequency or amount of watering does have the potential to be nullified. ... Conclusion. In conclusion, understanding and effectively formulating a solid hypothesis is what scientific ...
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Definition: Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation. Hypothesis is often used in scientific research to guide the design of experiments ...
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3. Simple hypothesis. A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, "Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking. 4.
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Step 5: Present your findings. The results of hypothesis testing will be presented in the results and discussion sections of your research paper, dissertation or thesis.. In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p-value).
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Examples of a complex hypothesis include: "People with high-sugar diets and sedentary activity levels are more likely to develop depression." "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."
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Another example for a directional one-tailed alternative hypothesis would be that. H1: Attending private classes before important exams has a positive effect on performance. Your null hypothesis would then be that. H0: Attending private classes before important exams has no/a negative effect on performance.
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CONCLUSION. The final step in the scientific method is the conclusion. This is a summary of the experiment's results, and how those results match up to your hypothesis. You have two options for your conclusions: based on your results, either: (1) YOU CAN REJECT the hypothesis, or (2) YOU CAN NOT REJECT the hypothesis. This is an important point!
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Examples. A research hypothesis, in its plural form "hypotheses," is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.
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15 Hypothesis Examples. A hypothesis is defined as a testable prediction, and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022). In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis ...
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Step 2: Collect the data. The next step is to obtain a sample and collect data that will allow the researcher to test the hypotheses. The sample must be representative of the population and, ideally, should be a random sample. In this case, the researcher must randomly sample teens who use smart phones. For the purposes of this example, imagine ...
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The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself. For example, if the claim was the alternative that the mean score on a test was greater than 85, and your decision was to Reject then Null, then you could conclude: " At the 5% significance level, there is sufficient ...
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Example 10.5.1 10.5. 1. Suppose a baker claims that his bread height is more than 15 cm, on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm.
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Onward! We use p -values to make conclusions in significance testing. More specifically, we compare the p -value to a significance level α to make conclusions about our hypotheses. If the p -value is lower than the significance level we chose, then we reject the null hypothesis H 0 in favor of the alternative hypothesis H a .
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This makes the data analyst use judgment rather than mindlessly applying rules. The following examples illustrate a left-, right-, and two-tailed test. Example 9.5.1. H0: μ = 5, Ha: μ < 5. Test of a single population mean. Ha tells you the test is left-tailed. The picture of the p -value is as follows: Figure 9.5.1.
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Answer link. Well, an hypothesis is something that is proposed.... And the mark of a good "hypothesis" is its "testability". That is there exist a few simple experiments whose results would confirm or deny the original hypothesis. And a conclusion is drawn AFTER the experiment is performed, and reports whether or not the results of the ...

How to Write Hypothesis Test Conclusions (With Examples)

Example 1: Reject the Null Hypothesis Conclusion

Example 2: Fail to Reject the Null Hypothesis Conclusion

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Published by Zach

How to Write Hypothesis Test Conclusions (With Examples)

Example 1: Reject the Null Hypothesis Conclusion

Example 2: Fail to Reject the Null Hypothesis Conclusion

Additional Resources

10 Examples of Using Probability in Real Life

What is a Hypothesis – Types, Examples and Writing Guide

Types of Hypothesis

Research Hypothesis

Null Hypothesis

Alternative Hypothesis

Directional Hypothesis

Non-directional Hypothesis

Statistical Hypothesis

Composite Hypothesis

Empirical Hypothesis

Simple Hypothesis

Complex Hypothesis

Applications of Hypothesis

How to write a Hypothesis

Identify the Research Question

Conduct a Literature Review

Determine the Variables

Formulate the Hypothesis

Write the Null Hypothesis

Refine the Hypothesis

Examples of Hypothesis

Purpose of Hypothesis

When to use Hypothesis

Characteristics of Hypothesis

Advantages of Hypothesis

Limitations of Hypothesis

About the author

Muhammad Hassan

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Table of Contents

What is a Hypothesis?

Different Types of Hypotheses‌

1. Null hypothesis

2. Alternative hypothesis

3. Simple hypothesis

4. Complex hypothesis

5. Associative and casual hypothesis

6. Empirical hypothesis

7. Statistical hypothesis

Characteristics of a Good Hypothesis

Separating a Hypothesis from a Prediction

Finally, How to Write a Hypothesis

1. Be clear about your research question

2. Carry out a recce

3. Create a 3-dimensional hypothesis

4. Write the first draft

5. Proof your hypothesis

Frequently Asked Questions (FAQs)

2. What is an example of hypothesis?

3. What is an example of null hypothesis?

4. What are the types of research?

5. How to write a hypothesis?

6. What are the 2 types of hypothesis?

7. Difference between research question and research hypothesis?

8. What is plural for hypothesis?

9. What is the red queen hypothesis?

10. Who is known as the father of null hypothesis?

11. When to reject null hypothesis?

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