Null Hypothesis

Hypothesis Definition 

  • In Statistics, a hypothesis can be defined as a formal statement, which gives the explanation about the relationship between any two or more variables of the specified population. 

  • Hypothesis helps the researcher to translate any given problem to a clear explanation for the outcome of the study.

  •  Hypothesis clearly explains and predicts the expected outcome and it indicates the types of experimental design and directs the study of any research process.

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What Is The Null Hypothesis?

Let’s know the null hypothesis definition,

  • We can define null hypothesis as a general statement or a default position that says there is no relationship between two measured phenomena or there is no association among groups.

  • In statistics, null hypothesis is denoted H0 and is pronounced as "H-nought" or "H-null", or "H-zero" with the subscript being the digit equal to 0.

Why is Null Hypothesis Important?

  • Hypothesis helps the researcher to translate any given problem to a clear explanation for the outcome of the study.

  • Testing (which involves accepting, approving, rejecting, or disproving) the null hypothesis and thus concluding that there are or we can say that there are no grounds for believing that there is any relationship between two phenomena is basically a central task in the modern practice of science; in the field of statistics.

  • To be more specific, hypothesis testing gives precise criteria for rejecting or accepting a null hypothesis within a level known as the confidence level.

Null Hypothesis Symbol-

His the null hypothesis symbol that is used in statistics.

  • In statistics, null hypothesis symbol is denoted H0 and is pronounced as "H-nought" or "H-null", or "H-zero" with the subscript being the digit equal to 0.

How Do You State a Null Hypothesis?

Problem: A researcher thinks that if the knee surgery patients go to physical therapy twice a week (instead of going 3 times), their recovery period will be longer. Given average recovery time knee surgery patients given is 8.2 weeks. 

Step 1: First we need to figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem that you need to figure out. The hypothesis that has being given in above question is “I expect the average recovery period to be greater than 8.2 weeks.”

Step 2: You need to convert the hypothesis to math. Remember that the average can be sometimes written as μ.

H1: μ > 8.2(average)

Step 3: Now state what will happen if the hypothesis doesn’t come true. If the recovery time is not greater than the given average that is 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or it is less than 8.2 weeks.

H0: μ ≤ 8.2

H(The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

Null Hypothesis Example-

As we have discussed the null hypothesis definition, let’s go through the examples.

  • Given the test scores of two any random samples, one sample of men and other of women, does one group differ from the other group? A possible null hypothesis says that the mean male score is the same as the mean female score:

  • H0 🡪 μ1 = μ2 where

H0 is the null hypothesis,

μ1 is the mean of population 1, and

μ2 is the mean of population 2.

  • A stronger null hypothesis denotes that if two samples are drawn from the same given population, such that the variances and shapes of the given distributions are also equal.

Null Hypothesis Principle and When is A Null Hypothesis Rejected?

The principle followed for null hypothesis testing is basically collecting the data and determining the chances of a given set of data during the study on any given random sample, assuming that the null hypothesis is true.

 If suppose that the given data does not face the expected null hypothesis, then the outcome we will get will be quite weaker and they conclude that by saying that the given set of data does not provide strong evidence against the null hypothesis which is because of insufficient evidence. Finally, this leads to null hypothesis rejection.

Null Hypothesis Example-

  • There may be a possibility of getting deceased by typhoid but the possibility may not 100%.

  • There is no age limit to using mobile phones so that a person can access the internet.

  • Having an apple a day does not obviously confirm not getting a fever, but apple helps to boost immunity to fight against the disease.

Null Hypothesis Formula or How Do You Find The Null Hypothesis :

Let’s discuss the null hypothesis formula:

Here, the null hypothesis formula are given below.

The formula for the null hypothesis can be written:

H0:  p = p0

The formula for the alternative hypothesis can be written as:

Ha = p >p0, and < p0≠ p0

The formula for the test static is denoted by:

Z =  \[\frac{P - P_{0}}{\sqrt{\frac{P_{0}(1 - P_{0})}{n}}}\] 


Remember that, phere is the null hypothesis.

Examples of Null Hypothesis:

Here are some of the examples. These examples will help you understand the concept of null hypothesis in a better way. You will understand what leads to null hypothesis rejection.

If suppose there is a medicine that reduces the risk of cardiac stroke, then the null hypothesis should be “that the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a specific group of people in a controlled way. If the survey shows that there is a significant change in the people, then this leads to null hypothesis rejection.

Few more examples let’s see the examples listed down:

1). Is there a 100% chance of getting affected by dengue?

Answer: There could be chances of getting affected by dengue but the chances of getting affected by dengue are not 100%.

2). Do teenagers these days use mobile phones more than adults to access the internet?

Answer: Age has no limit and is not a factor that we can use mobile phones to access the internet.

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

Answer: Having apple daily does not assure of not having fever, but on the other hand it does increase the immunity to fight against such diseases.

4). Are children better in performing mathematical calculations than adults?

Answer: Again in this example too, age has no effect on Mathematical skills.

FAQ (Frequently Asked Questions)

1. What is a null hypothesis example and how to reject a null hypothesis?

null hypothesis can be defined as a hypothesis that says there is no statistical significance between any two variables in the hypothesis. For example, Susie’s null hypothesis would be something like this: There is no statistically significant relationship between the type of water I feed the different flowers and the growth of the flowers.The convention in most biological research is to use a significance level of basically 0.05. This means that if the value of P is less than the value 0.05, you basically reject the null hypothesis; if the value of P is greater than or equal to 0.05, you don't reject the null hypothesis.

2. Why is a null hypothesis important and can you accept a null hypothesis?

The purpose and the importance of the null hypothesis and alternative hypothesis are that they provide an approximate description of any given phenomena. The purpose of null hypothesis is to provide the researcher or an investigator with the relational statement that is directly tested in any research study. Null hypothesis is a hypothesis which is never accepted. We either reject them or we fail to reject them. Hence, failing to reject the null hypothesis does not mean that we have shown that there is no difference that is accepting the null hypothesis.