Statistics Made Easy
How to Write a Null Hypothesis (5 Examples)
A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:
H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value
H A (Alternative Hypothesis): Population parameter <, >, ≠ some value
Note that the null hypothesis always contains the equal sign .
We interpret the hypotheses as follows:
Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.
Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.
For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.
To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:
H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)
H A : μ > 20 (the true mean height of plants is greater than 20 inches)
If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.
Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.
Example 1: Weight of Turtles
A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.
Here is how to write the null and alternative hypotheses for this scenario:
H 0 : μ = 300 (the true mean weight is equal to 300 pounds)
H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)
Example 2: Height of Males
It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.
H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)
H A : μ > 68 (the true mean height is greater than 68 inches)
Example 3: Graduation Rates
A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.
H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)
H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)
Example 4: Burger Weights
A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.
H 0 : μ = 7 (the true mean weight is equal to 7 ounces)
H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)
Example 5: Citizen Support
A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.
H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)
H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)
Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance
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Null Hypothesis Definition and Examples
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In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis.
The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a non-random factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .
How to State a Null Hypothesis
There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.
For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.
The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."
This can be written mathematically as: H 1 : μ > 6
In this example, μ is the average.
Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:
H 0 : μ ≤ 6
The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:
H 0 : μ = 6
Null Hypothesis Examples
"Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.
Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.
Why Test a Null Hypothesis?
You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.
For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.
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Unit 10: lesson 3.
- Idea behind hypothesis testing
Examples of null and alternative hypotheses
- P-values and significance tests
- Comparing P-values to different significance levels
- Estimating a P-value from a simulation
- Using P-values to make conclusions
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- How to Write a Strong Hypothesis | Steps & Examples
How to Write a Strong Hypothesis | Steps & Examples
Published on May 6, 2022 by Shona McCombes . Revised on December 2, 2022.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .
Daily apple consumption leads to fewer doctor’s visits.
Table of contents
What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Variables in hypotheses
Hypotheses propose a relationship between two or more types of variables .
- An independent variable is something the researcher changes or controls.
- A dependent variable is something the researcher observes and measures.
If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.
In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .
Step 1. Ask a question
Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.
Step 2. Do some preliminary research
Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.
At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.
Step 3. Formulate your hypothesis
Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.
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. Phrase your hypothesis in three ways
To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.
In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.
If you are comparing two groups, the hypothesis can state what difference you expect to find between them.
6. Write a null hypothesis
If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .
- H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
- H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.
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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
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We interpret the hypotheses as follows: Null hypothesis: The sample data provides no evidence to support some claim being made by an individual. Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.
There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement. For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged.
The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a change, difference, or relationship.
The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a. H0: The number of lectures attended by first-year students has no effect on their final exam scores.