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## What Is a Null Hypothesis?

How a null hypothesis works, the alternative hypothesis, examples of a null hypothesis.

## Null Hypothesis: What Is It and How Is It Used in Investing?

## Key Takeaways

- A null hypothesis is a type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.
- The alternative hypothesis proposes that there is a difference.
- Hypothesis testing provides a method to reject a null hypothesis within a certain confidence level.
- If you can reject the null hypothesis, it provides support for the alternative hypothesis.
- Null hypothesis testing is the basis of the principle of falsification in science.

## Null Hypothesis

A null hypothesis can only be rejected, not proven.

For the above examples, the alternative hypothesis would be:

- Students score an average that is not equal to seven.
- The mean annual return of the mutual fund is not equal to 8% per year.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

For the above examples, null hypotheses are:

- Example A : Students in the school score an average of seven out of 10 in exams.
- Example B: Mean annual return of the mutual fund is 8% per year.

## How Null Hypothesis Testing Is Used in Investments

## How Is the Null Hypothesis Identified?

## How Is Null Hypothesis Used in Finance?

## How Are Statistical Hypotheses Tested?

## What Is an Alternative Hypothesis?

Sage Publishing. " Chapter 8: Introduction to Hypothesis Testing ," Pages 4–7.

Sage Publishing. " Chapter 8: Introduction to Hypothesis Testing ," Page 4.

Sage Publishing. " Chapter 8: Introduction to Hypothesis Testing ," Page 7.

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## What Is the Null Hypothesis?

## Examples of the Null Hypothesis

## Null Hypothesis Definition

## What Is a Null Hypothesis?

There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.

There are statistical relationships among the forms of water that are given to plants for growth and nourishment.

The example below shows the difference between null vs alternative hypotheses:

Alternate Hypothesis: The world is round Null Hypothesis: The world is not round.

The alternative and null hypothesis for Susie’s assumption is:

- Null Hypothesis: If one plant is watered with distilled water and the other with mineral water, then there is no difference in the growth and nourishment of these two plants.
- Alternative Hypothesis: If one plant is watered with distilled water and the other with mineral water, then the plant with mineral water shows better growth and nourishment.

Why do we need to assess it? Why not just verify an alternate one?

## Development of the Null

Writing a null hypothesis consists of two steps:

- Firstly, initiate by asking a question.
- Secondly, restate the question in such a way that it seems there are no relationships among the variables.

In other words, assume in such a way that the treatment does not have any effect.

The usual recovery duration after knee surgery is considered almost 8 weeks.

“The expected recovery period in knee rehabilitation is more than 8 weeks”

There are two options: either the recovery will be less than or equal to 8 weeks.

What will happen if the scientist does not have any knowledge about the outcome?

## Significance Tests

The following table will explain the symbols:

P-value is the chief statistical final result of the significance test of the null hypothesis.

- P-value = Pr(data or data more extreme | H 0 true)
- | = “given”
- Pr = probability
- H 0 = the null hypothesis

When to reject the null hypothesis?

H 0 :p= the value of p if H 0 is true

P = assume value if H 0 proves true.

Step 3: Find out the value of P. P-value is the probability of data that is under observation.

Rise or increase in the P value = Pr(X ≥ x)

X = observed number of successes

Step 4: Demonstrate the findings or outcomes in a descriptive detailed way.

## Perceived Problems With the Null Hypothesis

The main point about the definition is: Observed results are not based on a-value

## Null Hypothesis Examples

## Example 1: Hypotheses with One Sample of One Categorical Variable

- Research Question: Do artists more expected to be left-handed as compared to the common population persons in society?
- Response Variable: Sorting the student into two categories. One category has left-handed persons and the other category have right-handed persons.
- Form Null Hypothesis: Arts and Architecture college students are no more predicted to be lefty as compared to the common population persons in society (Lefty students of Arts and Architecture college population is 10% or p= 0.10)

## Example 2: Hypotheses with One Sample of One Measurement Variable

- Research Question: Does the statistical data recommended about the mean and average dosage of the population differ from 50mg?
- Response Variable: Chemical assay used to find the appropriate dosage of the active ingredient.
- Null Hypothesis: Usually, the 50mg dosage of capsules of this trade name (population average and means dosage =50 mg).

## Example 3: Hypotheses with Two Samples of One Categorical Variable

- Research Question: Does the data recommend that females (women) prefer vegetarian meals more than males (men) regularly?
- Response Variable: Cataloguing the persons into vegetarian and non-vegetarian categories. Grouping Variable: Gender
- Null Hypothesis: Gender is not linked to those who like vegetarian meals. (Population percent of women who eat vegetarian meals regularly = population percent of men who eat vegetarian meals regularly or p women = p men).

## Example 4: Hypotheses with Two Samples of One Measurement Variable

- Research Question: Does the given data recommend that usually, a low-carbohydrate diet helps in losing weight faster as compared to a low-fat diet?
- Response Variable: Weight loss (pounds)
- Explanatory Variable: Form of diet either low carbohydrate or low fat
- Null Hypothesis: There is no significant difference when comparing the mean loss of weight of people using a low carbohydrate diet to people using a diet having low fat. (population means loss of weight on a low carbohydrate diet = population means loss of weight on a diet containing low fat).

## Example 5: Hypotheses about the relationship between Two Categorical Variables

- Research Question: Did second-hand smoke enhance the chances of stroke?
- Variables: There are 02 diverse categories of variables. (Controls and stroke patients) (whether the smoker lives in the same house). The chances of having a stroke will be increased if a person is living with a smoker.
- Null Hypothesis: There is no significant relationship between a passive smoker and stroke or brain attack. (odds ratio between stroke and the passive smoker is equal to 1).

## Example 6: Hypotheses about the relationship between Two Measurement Variables

- Response variable- Regular alteration in price
- Explanatory Variable- Stock bought by non-management employees
- Null Hypothesis: The association and relationship between the regular stock price alteration ($) and the daily stock-buying by non-management employees ($) = 0.

## Example 7: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples

- Research Question: Is the relation between the bill paid in a restaurant and the tip given to the waiter, is linear? Is this relation different for dining and family restaurants?
- Explanatory Variable- total bill amount
- Response Variable- the amount of tip
- Null Hypothesis: The relationship and association between the total bill quantity at a family or dining restaurant and the tip, is the same.

Try to answer the quiz below to check what you have learned so far about the null hypothesis.

## Send Your Results (Optional)

- Blackwelder, W. C. (1982). “Proving the null hypothesis” in clinical trials. Controlled Clinical Trials , 3(4), 345–353.
- Frick, R. W. (1995). Accepting the null hypothesis. Memory & Cognition, 23(1), 132–138.
- Gill, J. (1999). The insignificance of null hypothesis significance testing. Political Research Quarterly , 52(3), 647–674.
- Killeen, P. R. (2005). An alternative to null-hypothesis significance tests. Psychological Science, 16(5), 345–353.

©BiologyOnline.com. Content provided and moderated by Biology Online Editors.

Last updated on June 16th, 2022

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## Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

Mathematical Symbols Used in H 0 and H a :

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

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

## Concept Review

## Formula Review

H 0 and H a are contradictory.

- OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/30189442-6998-[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

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## Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on December 6, 2022.

- 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

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

## Examples of null hypotheses

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

Discover proofreading & editing

## Examples of alternative hypotheses

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.

## General template sentences

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

## Cite this Scribbr article

Turney, S. (2022, December 06). Null & Alternative Hypotheses | Definitions, Templates & Examples. Scribbr. Retrieved February 27, 2023, from https://www.scribbr.com/statistics/null-and-alternative-hypotheses/

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## Null Hypothesis Examples Recently updated !

- The null hypothesis is a nullifiable hypothesis. A researcher seeks to reject it because this result strongly indicates observed differences are real and not just due to chance.
- The null hypothesis may be accepted or rejected, but not proven. There is always a level of confidence in the outcome.

## What Is the Null Hypothesis?

## Exact and Inexact Null Hypothesis

Both groups have value of 100 (or any number or quality) H 0 : μ = 100

Recovery time from a treatment is the same or worse than a placebo: H 0 : μ ≥ placebo time

There is a 5% or less difference between two groups: H 0 : 95 ≤ μ ≤ 105

## How to State the Null Hypothesis

- State the goal of the experiment: “I hope the average recovery time with the new drug will be less than 3 weeks.”
- Rephrase the hypothesis to assume the treatment has no effect: “If the drug doesn’t shorten recovery time, then the average time will be 3 weeks or longer.” Mathematically: H 0 : μ ≥ 3

Of course, the researcher could test the no-effect hypothesis (exact null hypothesis): H 0 : μ = 3

H A : μ ≠ 3 (which includes μ <3 and μ >3)

## Null Hypothesis Examples

- Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007). Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing. ISBN 978-90-79418-01-5 .
- Cox, D. R. (2006). Principles of Statistical Inference . Cambridge University Press. ISBN 978-0-521-68567-2 .
- Everitt, Brian (1998). The Cambridge Dictionary of Statistics . Cambridge, UK New York: Cambridge University Press. ISBN 978-0521593465.
- Weiss, Neil A. (1999). Introductory Statistics (5th ed.). ISBN 9780201598773.

## Related Posts

## Null Hypothesis

## Null Hypothesis Definition

## Null Hypothesis Symbol

## Null Hypothesis Principle

## Null Hypothesis Formula

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

The formula for the alternative hypothesis is:

The formula for the test static is:

Remember that, p 0 is the null hypothesis and p – hat is the sample proportion.

## Types of Null Hypothesis

There are different types of hypothesis. They are:

The composite hypothesis is one that does not completely specify the population distribution.

Exact hypothesis defines the exact value of the parameter. For example μ= 50

## Null Hypothesis Rejection

## How do you Find the Null Hypothesis?

## When is Null Hypothesis Rejected?

## Null Hypothesis and Alternative Hypothesis

Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.

## Null Hypothesis Examples

1). Are there is 100% chance of getting affected by dengue?

Ans: There could be chances of getting affected by dengue but not 100%.

2). Do teenagers are using mobile phones more than grown-ups to access the internet?

Ans: Age has no limit on using mobile phones to access the internet.

3). Does having apple daily will not cause fever?

4). Do the children more good in doing mathematical calculations than grown-ups?

Ans: Age has no effect on Mathematical skills.

## Frequently Asked Questions on Null Hypothesis

What is meant by the null hypothesis.

## What are the benefits of hypothesis testing?

## When a null hypothesis is accepted and rejected?

## Why is the null hypothesis important?

## How to accept or reject the null hypothesis in the chi-square test?

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

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The hypothesis is called the null hypothesis, or simply "the null".

## The null is like the defendant in a criminal trial

This process resembles a trial:

the defendant (the null hypothesis) is accused of being guilty (wrong);

evidence (data) is gathered in order to prove the defendant guilty (reject the null);

otherwise, the defendant is found not guilty (the null is not rejected).

Then, the data is collected and used to compute the value of the test statistic.

A decision is taken as follows:

if the test statistic falls within the rejection region, then the null hypothesis is rejected;

otherwise, it is not rejected.

We now make two examples of practical problems that lead to formulate and test a null hypothesis.

A new method is proposed to produce light bulbs.

The proponents claim that it produces less defective bulbs than the method currently in use.

To check the claim, we can set up a statistical test as follows.

50 of them are produced with the new method (group A)

the remaining 50 are produced with the old method (group B).

The final data comprises 100 observations of:

a categorical variable that records the group (A or B) to which each light bulb belongs.

We use the data to compute the proportions of working light bulbs in groups A and B.

We then compute a z-statistic (see here for details) by:

taking the difference between the proportion in group A and the proportion in group B;

we subtract the expected value (which is zero under the null hypothesis);

we divide by the standard deviation (it can be derived analytically).

The distribution of the z-statistic can be approximated by a standard normal distribution .

A statistical test is set up as follows.

The reliability of the plant is measured by the number of halts.

The manager cannot wait more than one year before taking a decision.

There will be a single datum at his disposal: the number of halts observed during one year.

The manager decides that the probability of incorrectly rejecting the null can be at most 10%.

A Poisson random variable with expected value equal to 1 takes values:

larger than 1 with probability 26.42%;

larger than 2 with probability 8.03%.

Failure to reject is interpreted as insufficient evidence that the plant is unreliable.

Does this mean that we accept the null? Not really.

In turn, lack of evidence can be due:

either to the fact that the defendant is innocent ;

Let's consider the first of the two examples above (the production of light bulbs).

How much is the ex-ante probability of rejecting the null if the alternative hypothesis is true?

the main assumption (the one we are testing);

What we said can be summarized in the following guiding principles:

More examples of null hypotheses and how to test them can be found in the following lectures.

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The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the

Examples of the Null Hypothesis ; Do cats care about the color of their food? Cats express no food preference based on color. ; Does chewing

How to State the Null Hypothesis ... Example Problem: A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3 times)

Null Hypothesis: If one plant is watered with distilled water and the other with mineral water, then there is no difference in the growth and

For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the

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

Examples of null hypotheses ; Research question · General, Test-specific ; Does tooth flossing affect the number of cavities? Tooth flossing has no

The null hypothesis assumes no difference between two groups or that the independent variable has no effect on the dependent variable.

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening.

In that example, the null hypothesis is: the probability that a light bulb is defective does not decrease after introducing a new production method. Let's make