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• Null and Alternative Hypotheses | Definitions & Examples

Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis ( H 0 ): There’s no effect in the population .
• Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:

• The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
• The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

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The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis ( H a ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question.
• They both make claims about the population.
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

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To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

General template sentences

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
• Alternative hypothesis ( H a ): Independent variable affects dependent variable.

Test-specific template sentences

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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.

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.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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What is an Alternative Hypothesis in Statistics?

Often in statistics we want to test whether or not some assumption is true about a population parameter .

For example, we might assume that the mean weight of a certain population of turtle is 300 pounds.

To determine if this assumption is true, we’ll go out and collect a sample of turtles and weigh each of them. Using this sample data, we’ll conduct a hypothesis test .

The first step in a hypothesis test is to define the  null and  alternative hypotheses .

These two hypotheses need to be mutually exclusive, so if one is true then the other must be false.

These two hypotheses are defined as follows:

Null hypothesis (H 0 ): The sample data is consistent with the prevailing belief about the population parameter.

Alternative hypothesis (H A ): The sample data suggests that the assumption made in the null hypothesis is not true. In other words, there is some non-random cause influencing the data.

Types of Alternative Hypotheses

There are two types of alternative hypotheses:

A  one-tailed hypothesis involves making a “greater than” or “less than ” statement. For example, suppose we assume the mean height of a male in the U.S. is greater than or equal to 70 inches.

The null and alternative hypotheses in this case would be:

• Null hypothesis: µ ≥ 70 inches
• Alternative hypothesis: µ < 70 inches

A  two-tailed hypothesis involves making an “equal to” or “not equal to” statement. For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches.

• Null hypothesis: µ = 70 inches
• Alternative hypothesis: µ ≠ 70 inches

Note: The “equal” sign is always included in the null hypothesis, whether it is =, ≥, or ≤.

Examples of Alternative Hypotheses

The following examples illustrate how to define the null and alternative hypotheses for different research problems.

Example 1: A biologist wants to test if the mean weight of a certain population of turtle is different from the widely-accepted mean weight of 300 pounds.

The null and alternative hypothesis for this research study would be:

• Null hypothesis: µ = 300 pounds
• Alternative hypothesis: µ ≠ 300 pounds

If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean weight of this population of turtles is different from 300 pounds.

Example 2: An engineer wants to test whether a new battery can produce higher mean watts than the current industry standard of 50 watts.

• Null hypothesis: µ ≤ 50 watts
• Alternative hypothesis: µ > 50 watts

If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean watts produced by the new battery is greater than the current industry standard of 50 watts.

Example 3: A botanist wants to know if a new gardening method produces less waste than the standard gardening method that produces 20 pounds of waste.

• Null hypothesis: µ ≥ 20 pounds
• Alternative hypothesis: µ < 20 pounds

If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean weight produced by this new gardening method is less than 20 pounds.

When to Reject the Null Hypothesis

Whenever we conduct a hypothesis test, we use sample data to calculate a test-statistic and a corresponding p-value.

If the p-value is less than some significance level (common choices are 0.10, 0.05, and 0.01), then we reject the null hypothesis.

This means we have sufficient evidence from the sample data to say that the assumption made by the null hypothesis is not true.

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

This means our sample data did not provide us with evidence that the assumption made by the null hypothesis was not true.

Additional Resource:   An Explanation of P-Values and Statistical Significance

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9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

• Describe hypothesis testing in general and in practice

The actual test begins by considering two  hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H a : The alternative hypothesis : It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make adecision. There are two options for a  decision . They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in  H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66

• H 0 : μ = 66
• H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45

• H 0 : μ ≥ 45
• H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p ≤ 0.066

H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40

• H 0 : p = 0.40
• H a : p > 0.40

Concept Review

In a  hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

H 0 and H a are contradictory.

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8.2 Null and Alternative Hypotheses

Learning objectives.

• Describe hypothesis testing in general and in practice.

A hypothesis test begins by considering two hypotheses .  They are called the null hypothesis and the alternative hypothesis .  These hypotheses contain opposing viewpoints and only one of these hypotheses is true.  The hypothesis test determines which hypothesis is most likely true.

• The null hypothesis is a claim that a population parameter equals some value.  For example, [latex]H_0: \mu=5[/latex].
• The alternative hypothesis is a claim that a population parameter is greater than, less than, or not equal to some value.  For example, [latex]H_a: \mu>5[/latex], [latex]H_a: \mu<5[/latex], or [latex]H_a: \mu \neq 5[/latex].  The form of the alternative hypothesis depends on the wording of the hypothesis test.
• An alternative notation for [latex]H_a[/latex] is [latex]H_1[/latex].

Because the null and alternative hypotheses are contradictory, we must examine evidence to decide if we have enough evidence to reject the null hypothesis or not reject the null hypothesis.  The evidence is in the form of sample data.  After we have determined which hypothesis the sample data supports, we make a decision.  There are two options for a decision . They are “ reject [latex]H_0[/latex] ” if the sample information favors the alternative hypothesis or “ do not reject [latex]H_0[/latex] ” if the sample information is insufficient to reject the null hypothesis.

Watch this video: Simple hypothesis testing | Probability and Statistics | Khan Academy by Khan Academy [6:24]

A candidate in a local election claims that 30% of registered voters voted in a recent election.  Information provided by the returning office suggests that the percentage is higher than the 30% claimed.

The parameter under study is the proportion of registered voters, so we use [latex]p[/latex] in the statements of the hypotheses.  The hypotheses are

[latex]\begin{eqnarray*} \\ H_0: & & p=30\% \\ \\ H_a: & & p \gt 30\% \\ \\ \end{eqnarray*}[/latex]

• The null hypothesis [latex]H_0[/latex] is the claim that the proportion of registered voters that voted equals 30%.
• The alternative hypothesis [latex]H_a[/latex] is the claim that the proportion of registered voters that voted is greater than (i.e. higher) than 30%.

A medical researcher believes that a new medicine reduces cholesterol by 25%.  A medical trial suggests that the percent reduction is different than claimed.  State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & p=25\% \\ \\ H_a: & & p \neq 25\% \end{eqnarray*}[/latex]

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0).  State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & \mu=2  \mbox{ points} \\ \\ H_a: & & \mu \neq 2 \mbox{ points}  \end{eqnarray*}[/latex]

We want to test whether or not the mean height of eighth graders is 66 inches.  State the null and alternative hypotheses.

[latex]\begin{eqnarray*}  H_0: & & \mu=66 \mbox{ inches} \\ \\ H_a: & & \mu \neq 66 \mbox{ inches}  \end{eqnarray*}[/latex]

We want to test if college students take less than five years to graduate from college, on the average.  The null and alternative hypotheses are:

[latex]\begin{eqnarray*} H_0: & & \mu=5 \mbox{ years} \\ \\ H_a: & & \mu \lt 5 \mbox{ years}   \end{eqnarray*}[/latex]

We want to test if it takes fewer than 45 minutes to teach a lesson plan.  State the null and alternative hypotheses.

[latex]\begin{eqnarray*}  H_0: & & \mu=45 \mbox{ minutes} \\ \\ H_a: & & \mu \lt 45 \mbox{ minutes}  \end{eqnarray*}[/latex]

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass.  The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass.  Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%.  State the null and alternative hypotheses.

[latex]\begin{eqnarray*}  H_0: & & p=6.6\% \\ \\ H_a: & & p \gt 6.6\%  \end{eqnarray*}[/latex]

On a state driver’s test, about 40% pass the test on the first try.  We want to test if more than 40% pass on the first try.   State the null and alternative hypotheses.

[latex]\begin{eqnarray*}  H_0: & & p=40\% \\ \\ H_a: & & p \gt 40\%  \end{eqnarray*}[/latex]

Concept Review

In a  hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim.  If certain conditions about the sample are satisfied, then the claim can be evaluated for a population.  In a hypothesis test, we evaluate the null hypothesis , typically denoted with [latex]H_0[/latex]. The null hypothesis is not rejected unless the hypothesis test shows otherwise.  The null hypothesis always contain an equal sign ([latex]=[/latex]).  Always write the alternative hypothesis , typically denoted with [latex]H_a[/latex] or [latex]H_1[/latex], using less than, greater than, or not equals symbols ([latex]\lt[/latex], [latex]\gt[/latex], [latex]\neq[/latex]).  If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.  But we can never state that a claim is proven true or false.  All we can conclude from the hypothesis test is which of the hypothesis is most likely true.  Because the underlying facts about hypothesis testing is based on probability laws, we can talk only in terms of non-absolute certainties.

Attribution

“ 9.1   Null and Alternative Hypotheses “ in Introductory Statistics by OpenStax  is licensed under a  Creative Commons Attribution 4.0 International License.

Introduction to Statistics Copyright © 2022 by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Alternative hypothesis

by Marco Taboga , PhD

In a statistical test, observed data is used to decide whether or not to reject a restriction on the data-generating probability distribution.

The assumption that the restriction is true is called null hypothesis , while the statement that the restriction is not true is called alternative hypothesis.

A correct specification of the alternative hypothesis is essential to decide between one-tailed and two-tailed tests.

Table of contents

Mathematical setting

Choice between one-tailed and two-tailed tests, the critical region, the interpretation of the rejection, the interpretation must be coherent with the alternative hypothesis.

• Power function

Accepting the alternative

More details, keep reading the glossary.

In order to fully understand the concept of alternative hypothesis, we need to remember the essential elements of a statistical inference problem:

we observe a sample drawn from an unknown probability distribution;

in principle, any valid probability distribution could have generated the sample;

however, we usually place some a priori restrictions on the set of possible data-generating distributions;

A couple of simple examples follow.

When we conduct a statistical test, we formulate a null hypothesis as a restriction on the statistical model.

The alternative hypothesis is

The alternative hypothesis is used to decide whether a test should be one-tailed or two-tailed.

The null hypothesis is rejected if the test statistic falls within a critical region that has been chosen by the statistician.

The critical region is a set of values that may comprise:

only the left tail of the distribution or only the right tail (one-tailed test);

both the left and the right tail (two-tailed test).

The choice of the critical region depends on the alternative hypothesis. Let us see why.

The interpretation is different depending on the tail of the distribution in which the test statistic falls.

The choice between a one-tailed or a two-tailed test needs to be done in such a way that the interpretation of a rejection is always coherent with the alternative hypothesis.

When we deal with the power function of a test, the term "alternative hypothesis" has a special meaning.

We conclude with a caveat about the interpretation of the outcome of a test of hypothesis.

The interpretation of a rejection of the null is controversial.

According to some statisticians, rejecting the null is equivalent to accepting the alternative.

However, others deem that rejecting the null does not necessarily imply accepting the alternative. In fact, it is possible to think of situations in which both hypotheses can be rejected. Let us see why.

According to the conceptual framework illustrated by the images above, there are three possibilities:

the null is true;

the alternative is true;

neither the null nor the alternative is true because the true data-generating distribution has been excluded from the statistical model (we say that the model is mis-specified).

If we are in case 3, accepting the alternative after a rejection of the null is an incorrect decision. Moreover, a second test in which the alternative becomes the new null may lead us to another rejection.

You can find more details about the alternative hypothesis in the lecture on Hypothesis testing .

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Statistics By Jim

Making statistics intuitive

Alternative hypothesis

By Jim Frost

The alternative hypothesis is one of two mutually exclusive hypotheses in a hypothesis test. The alternative hypothesis states that a population parameter does not equal a specified value. Typically, this value is the null hypothesis value associated with no effect , such as zero. If your sample contains sufficient evidence, you can reject the null hypothesis and favor the alternative hypothesis. The alternative hypothesis is often denoted as H 1 or H A .

If you are performing a two-tailed hypothesis test, the alternative hypothesis states that the population parameter does not equal the null hypothesis value. For example, when the alternative hypothesis is H A : μ ≠ 0, the test can detect differences both greater than and less than the null value.

A one-tailed alternative hypothesis can test for a difference only in one direction. For example, H A : μ > 0 can only test for differences that are greater than zero.

• How Hypothesis Tests Work: Significance Levels (Alpha) and P values
• How to Identify the Distribution of Your Data
• When Can I Use One-Tailed Hypothesis Tests?
• Examples of Hypothesis Tests: Busting Myths about the Battle of the Sexes
• Failing to Reject the Null Hypothesis

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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

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Video transcript