## Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

- Knowledge Base
- 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.

## Here's why students love Scribbr's proofreading services

Discover proofreading & editing

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.

( ) | ||

Does tooth flossing affect the number of cavities? | Tooth flossing has on the number of cavities. | test: The mean number of cavities per person does not differ between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ = µ . |

Does the amount of text highlighted in the textbook affect exam scores? | The amount of text highlighted in the textbook has on exam scores. | : There is no relationship between the amount of text highlighted and exam scores in the population; β = 0. |

Does daily meditation decrease the incidence of depression? | Daily meditation the incidence of depression.* | test: The proportion of people with depression in the daily-meditation group ( ) is greater than or equal to the no-meditation group ( ) in the population; ≥ . |

*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.

Does tooth flossing affect the number of cavities? | Tooth flossing has an on the number of cavities. | test: The mean number of cavities per person differs between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ ≠ µ . |

Does the amount of text highlighted in a textbook affect exam scores? | The amount of text highlighted in the textbook has an on exam scores. | : There is a relationship between the amount of text highlighted and exam scores in the population; β ≠ 0. |

Does daily meditation decrease the incidence of depression? | Daily meditation the incidence of depression. | test: The proportion of people with depression in the daily-meditation group ( ) is less than the no-meditation group ( ) in the population; < . |

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.

A claim that there is in the population. | A claim that there is in the population. | |

| ||

Equality symbol (=, ≥, or ≤) | Inequality symbol (≠, <, or >) | |

Rejected | Supported | |

Failed to reject | Not supported |

## Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

- Academic style
- Vague sentences
- Style consistency

See an example

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.

( ) | ||

test
with two groups | The mean dependent variable does not differ between group 1 (µ ) and group 2 (µ ) in the population; µ = µ . | The mean dependent variable differs between group 1 (µ ) and group 2 (µ ) in the population; µ ≠ µ . |

with three groups | The mean dependent variable does not differ between group 1 (µ ), group 2 (µ ), and group 3 (µ ) in the population; µ = µ = µ . | The mean dependent variable of group 1 (µ ), group 2 (µ ), and group 3 (µ ) are not all equal in the population. |

There is no correlation between independent variable and dependent variable in the population; ρ = 0. | There is a correlation between independent variable and dependent variable in the population; ρ ≠ 0. | |

There is no relationship between independent variable and dependent variable in the population; β = 0. | There is a relationship between independent variable and dependent variable in the population; β ≠ 0. | |

Two-proportions test | The dependent variable expressed as a proportion does not differ between group 1 ( ) and group 2 ( ) in the population; = . | The dependent variable expressed as a proportion differs between group 1 ( ) and group 2 ( ) in the population; ≠ . |

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.

## Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Turney, S. (2023, June 22). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved September 23, 2024, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/

## Is this article helpful?

## Shaun Turney

Other students also liked, inferential statistics | an easy introduction & examples, hypothesis testing | a step-by-step guide with easy examples, type i & type ii errors | differences, examples, visualizations, what is your plagiarism score.

## 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 :

equal (=) | not equal (≠) greater than (>) less than (<) |

greater than or equal to (≥) | less than (<) |

less than or equal to (≤) | more than (>) |

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.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

- Authors: Barbara Illowsky, Susan Dean
- Publisher/website: OpenStax
- Book title: Statistics
- Publication date: Mar 27, 2020
- Location: Houston, Texas
- Book URL: https://openstax.org/books/statistics/pages/1-introduction
- Section URL: https://openstax.org/books/statistics/pages/9-1-null-and-alternative-hypotheses

© Apr 16, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

## Have a thesis expert improve your writing

Check your thesis for plagiarism in 10 minutes, generate your apa citations for free.

- Knowledge Base
- Null and Alternative Hypotheses | Definitions & Examples

## Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

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 ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

## Table of contents

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

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.” On the other hand, 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.

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.

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 ≤).

## 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.

( ) | ||

Does tooth flossing affect the number of cavities? | Tooth flossing has on the number of cavities. | test: The mean number of cavities per person does not differ between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ = µ . |

Does the amount of text highlighted in the textbook affect exam scores? | The amount of text highlighted in the textbook has on exam scores. | : There is no relationship between the amount of text highlighted and exam scores in the population; β = 0. |

Does daily meditation decrease the incidence of depression? | Daily meditation the incidence of depression.* | test: The proportion of people with depression in the daily-meditation group ( ) is greater than or equal to the no-meditation group ( ) in the population; ≥ . |

*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.

Does tooth flossing affect the number of cavities? | Tooth flossing has an on the number of cavities. | test: The mean number of cavities per person differs between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ ≠ µ . |

Does the amount of text highlighted in a textbook affect exam scores? | The amount of text highlighted in the textbook has an on exam scores. | : There is a relationship between the amount of text highlighted and exam scores in the population; β ≠ 0. |

Does daily meditation decrease the incidence of depression? | Daily meditation the incidence of depression. | test: The proportion of people with depression in the daily-meditation group ( ) is less than the no-meditation group ( ) in the population; < . |

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.

A claim that there is in the population. | A claim that there is in the population. | |

| ||

Equality symbol (=, ≥, or ≤) | Inequality symbol (≠, <, or >) | |

Rejected | Supported | |

Failed to reject | Not supported |

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.

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

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.

( ) | ||

test
with two groups | The mean dependent variable does not differ between group 1 (µ ) and group 2 (µ ) in the population; µ = µ . | The mean dependent variable differs between group 1 (µ ) and group 2 (µ ) in the population; µ ≠ µ . |

with three groups | The mean dependent variable does not differ between group 1 (µ ), group 2 (µ ), and group 3 (µ ) in the population; µ = µ = µ . | The mean dependent variable of group 1 (µ ), group 2 (µ ), and group 3 (µ ) are not all equal in the population. |

There is no correlation between independent variable and dependent variable in the population; ρ = 0. | There is a correlation between independent variable and dependent variable in the population; ρ ≠ 0. | |

There is no relationship between independent variable and dependent variable in the population; β = 0. | There is a relationship between independent variable and dependent variable in the population; β ≠ 0. | |

Two-proportions test | The dependent variable expressed as a proportion does not differ between group 1 ( ) and group 2 ( ) in the population; = . | The dependent variable expressed as a proportion differs between group 1 ( ) and group 2 ( ) in the population; ≠ . |

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

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.

## Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

Turney, S. (2022, December 06). Null and Alternative Hypotheses | Definitions & Examples. Scribbr. Retrieved 23 September 2024, from https://www.scribbr.co.uk/stats/null-and-alternative-hypothesis/

## Is this article helpful?

## Shaun Turney

Other students also liked, levels of measurement: nominal, ordinal, interval, ratio, the standard normal distribution | calculator, examples & uses, types of variables in research | definitions & examples.

## 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 :

equal (=) | not equal (≠) greater than (>) less than (<) |

greater than or equal to (≥) | less than (<) |

less than or equal to (≤) | more than (>) |

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.

- OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
- Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
- Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

## IMAGES

## VIDEO

## COMMENTS

The null hypothesis. It is 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. The alternative hypothesis. It is a claim about the population that is contradictory to H0 and what we conclude when we ...

Study with Quizlet and memorize flashcards containing terms like The Null Hypothesis (Ho), The Alternative Hypothesis (Ha), Which of the following is true with respect to hypothesis testing? a. The null hypothesis Ho is assumed false. b. Action should be taken when the null hypothesis Ho is rejected. c. The alternative hypothesis Ha is assumed false. d. The alternative hypothesis Ho is assumed ...

Study with Quizlet and memorize flashcards containing terms like What is the null hypothesis?, What is the alternative hypothesis?, In scientific research the default assumption regarding the null and alternative hypotheses is? and more.

The Null Hypothesis: H0. 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. The Alternative Hypothesis: Ha. It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.

Alternative hypothesis. Alternative hypothesis \(\left(H_{A}\right)\): If we conclude that the null hypothesis is false, or rather and more precisely, we find that we provisionally fail to reject the null hypothesis, then we provisionally accept the alternative hypothesis.The view then is that something other than random chance has influenced the sample observations.

The null hypothesis (H0) answers "No, there's no effect in the population.". The alternative hypothesis (Ha) 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.

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.

Null Hypothesis (H0) the statistical hypothesis tested by the statistical procedure; usually a hypothesis of no difference or no relationship. (Ho, =,) alternative hypothesis (Ha) The hypothesis that states there is a difference between two or more sets of data. (Ha, <,>) left-tailed test. a test used on a hypothesis when the critical region is ...

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...

Study with Quizlet and memorize flashcards containing terms like Hypothesis Testing, hypothesis, Null Hypothesis and more.

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 of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in one tail of its sampling distribution. two-tailed test a test of the null hypothesis where the alternative hypothesis is not expressed directionally

H0: 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. Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0. Since the ...

Null and alternative hypothesis. Term. 1 / 10. Test value. Click the card to flip 👆. Definition. 1 / 10. The numerical value obtained from a statistical. Click the card to flip 👆.

Study with Quizlet and memorize flashcards containing terms like null hypothesis, alternative hypothesis, what symbols are used with the null hypothesis? and more.

Null hypothesis testing (4 steps) a statistical method that uses data from a sample to evaulate a hypothesis about a population. 1. State the hypotheses. Null hypothesis (Ho) ; in the general population, there is no change, no difference, or no relationship. Alternative hypothesis (H1) : there is a change, a difference, or relationship in the ...

Study with Quizlet and memorize flashcards containing terms like What are the two types of hypotheses used in a hypothesis test?, How are null and alternative hypothesis related?, A null hypothesis, Upper H 0 , is a and more.

Quiz yourself with questions and answers for Hypothesis Testing: Null and Alternative Hypotheses, so you can be ready for test day. Explore quizzes and practice tests created by teachers and students or create one from your course material.

You are designing a study to test the null hypothesis that μ = 0 \mu=0 μ = 0 versus the alternative that μ \mu μ is positive. Assume that σ \sigma σ is 15 . Suppose that it would be important to be able to detect the alternative μ = 2 \mu=2 μ = 2 Perform power calculations for a variety of sample sizes and determine how large a sample ...

b) The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge. The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. in our example: H 0: μ = 100 H_{0}:\mu = 100 H 0 : μ = 100 H a: μ < 100 H_{a}:\mu ...

The alternative hypothesis is a statement that is used in statistical inference experiments. It is in conflict with the null hypothesis and is indicated by the symbol H a H_a H a or H 1 H_1 H 1 . Alternatively, it can be referred to as a substitute for the null value. An alternative theory is a proposition that a researcher tests in hypothesis ...

Statistics. Question. (a) state the null and alternative hypotheses, and identify which represents the claim, (b) describe type I and type II errors for a hypothesis test of the claim, (c) explain whether the hypothesis test is left-tailed, or two-tailed, (d) explain how you should interpret a decision that rejects the null hypothesis, and (e ...

The null hypothesis states that there is no difference between a parameter and a specific value or that there is no difference between two parameters. The alternative hypothesis states that there is a specific difference between a parameter and a specific value or that there is a difference between two parameters. One possible example would be:

The null hypothesis states that the population parameter is equal to the given value. Thus the null hypothesis is. H 0: patameter = given value. \begin{aligned} H_0 &: \text{patameter}= \text{given value}. \end{aligned} H 0 : patameter = given value. For example, when testing whether the population mean is 50 50 50, the null hypothesis is ...