What is null and alternate hypothesis? Complete guide

The very first step of any hypothesis testing is to state the two important hypothetical conditions i.e. Null hypothesis and Alternate hypothesis. These two hypothetical condition defines the actual study which we want to do by performing hypothesis test.

While performing hypothesis testing, the researcher needs to convert the practical problem into the statistical problem and this process of conversion is nothing but defining the null and alternate hypothesis statement and then proceed further to perform testing.

In this article, We will understand the concept of null and alternate hypothesis and how to write them for any type of hypothesis testing with the help of some examples. At the end of this article, you can easily write these two conditions for any type of test. Let’s begin…

What is the null hypothesis?

The null hypothesis is the basic assumption behind doing any activity or it is an existing fact. During a hypothetical study, null hypothesis is the hypothesis that the researcher or analyst is trying to disprove. It is denoted by Ho or read as H-null, H-zero.

Its main purpose is to verify or disprove the proposed statistical assumptions. While performing hypothesis testing, we initially define the null and alternate hypothesis. The goal of any hypothesis test is to reject null or accept null hypothesis statements.

While performing the hypothetical study, if collected data doesn’t complete the expectation of null hypothesis then the final conclusion of the study would be that the data doesn’t provide sufficient evidence to support the null hypothesis hence it is rejected. 

On the other hand, if collected data completes the expectation of the null hypothesis then the final conclusion of the study would be that the data provide enough evidence to support the null hypothesis hence it fails to reject.

This decision-making of rejecting or accepting the null hypothesis is done with the help of the P-value. During hypothesis testing, we need to calculate the P-value and then compare it with the selected alpha level at the start of the study. Generally considered alpha level is 5% or 1%, etc. and then the decision has been done as per below standard criteria.

• If P-value >= 0.05 (alpha level) then failed to reject the null hypothesis.
• If P-value < 0.05 (alpha level) then reject null hypothesis.

Null hypothesis = Default assumptions

Examples of the null hypothesis –

Suppose the production manager wants to know whether the production rate of machines A and B is the same or it is different. Collect data and perform a hypothetical study to interpret the final result.

In this example, the default assumption the manager consider is that the production rate of machine A and B is same and then he goes for further analysis to test whether it is really same or not. Hence null hypothesis in this example is the production rates of machines A and B are equal i.e Ho: Ma = Mb.

Let’s see another example – Suppose a scientist for a company that manufactures processed food wants to assess the percentage of fat in the company’s bottled sauce. The advertised percentage is 18% and he measures the percentage of fat in 20 random samples. Wants to determine whether the fat percentage differs from 18%.

In this example, the default assumption the scientist considers is that the fat percentage is 18% and then he goes for further analysis to test whether it differs from 18%. Hence null hypothesis in this example is fat percentage is 18% i.e. Ho: µ = 18%.

I hope with these examples you got the basic idea of what is the null hypothesis and how to write it for any problem. Always remember Null hypothesis is associated with just equal to sign as Ho can either be accepted or rejected.

What is the Alternate hypothesis?

The alternate hypothesis is the research hypothesis or the claim that we want to test. During a hypothetical study, an alternate hypothesis is a hypothesis that the researcher or analyst is trying to prove. It is denoted by H1 or Ha and read as H-alternate.

During hypothesis testing, an alternate hypothesis is a hypothesis that is to be proved which indicates that the results of the test or research study are significant and the end result does not just occur by random chance, there has to be some non-random cause.

This statement or condition provides clarification to the hypothetical study as well as proper direction to study which then helps the analyst or problem solver to get required results from the study.

While performing the hypothetical study, if collected data doesn’t complete the expectation of the alternate hypothesis then the final conclusion of the study would be that the data doesn’t provide sufficient evidence to support the alternate hypothesis hence it is rejected. 

On the other hand, if collected data completes the expectation of the alternate hypothesis then the final conclusion of the study would be that the data provide enough evidence to support the alternate hypothesis hence it fails to reject.

One thing you should remember both the hypothetical conditions are not accepted or rejected at the same time. Only one condition is accepted or rejected at a time. For example, if the conclusion of the study is null hypothesis rejected then that means an alternate hypothesis is accepted and vice versa.

Similarly, this decision-making of rejecting or accepting the alternate hypothesis is done with the help of the P-value. As we discussed earlier for the null hypothesis, the calculated P-value has to be compared with an alpha level like 5% or 1% to make final conclusion.

So as per that same criteria,

• If P-value >= 0.05 (alpha level) then failed to reject the null hypothesis (means reject the alternate hypothesis.)
• If P-value < 0.05 (alpha level) then reject the null hypothesis (means fail to reject the alternate hypothesis.)

Alternate hypothesis = research hypothesis or claim to study

Examples of alternate hypothesis – 

Suppose the production manager wants to know whether the production rate of machines A and B is the same or it is different. Collect data and perform a hypothetical study to interpret the final result.

In this example, we already know the null hypothesis statement i.e. production rates of machines A and B are equal  (Ho: Ma = Mb). Alternate hypothesis means the claim that the manager wants to test so here the claim is, the production rate of machines A and B are not equal and this is an alternate hypothesis statement (Ha: Ma ≠ Mb).

• Ho: Ma = Mb
• Ha: Ma ≠ Mb

In 2nd example – Suppose a scientist for a company that manufactures processed food wants to assess the percentage of fat in the company’s bottled sauce. The advertised percentage is 18% and he measures the percentage of fat in 20 random samples. Wants to determine whether the fat percentage differs from 18%.

In this example also, we already know the null hypothesis is fat percentage is 18% i.e. Ho: µ = 18%. And the claim that scientist wants to test is whether the fat percentage differs from 18% or we can say it is not equal to 18%.i.e. (Ha: µ ≠ 18%).

• Ho: µ = 18%
• Ha: µ ≠ 18%

Always remember Alternate hypothesis is associated with equal to sign as well as a greater than or less than sign (for the one-tail test).

Both the example we discussed are of two-tailed test means in this example we are actually tested the claim in two directions but in one tail test we check the claim in one direction hence the alternate hypothesis condition is different for both one tail and two-tail test.

See one more example – 

Suppose a scientist for a company that manufactures processed food wants to assess the percentage of fat in the company’s bottled sauce. The advertised percentage is 18% and he measures the percentage of fat in 20 random samples. Wants to determine whether the fat percentage greater than 18%.

In this example, scientists want to test whether the fat percentage is greater than 18% (one direction testing) hence Ha: µ > 18%. (If the claim is fat percentage is less than 18% then alternate hypothesis statement will be like Ha: µ < 18%). 

Hypothetical conditions when the claim is fat percentage greater than 18%.

• Ho: µ = 18%
• Ha: µ > 18%

Hypothetical conditions when the claim is fat percentage less than 18%.

• Ho: µ = 18%
• Ha: µ < 18%

I hope you got the basic idea of what is the alternate hypothesis and how to write it for any problem. Now let’s compare these two hypothetical conditions and highlight some important points.

Difference between null and alternate hypothesis –

This comparison of the null and alternate hypothesis will provide you a quick summary of these two hypothetical conditions on the basis of different parameters. Let’s have a look at it – 

Conclusion – 

Defining Null and alternate hypothesis is the first step of any hypothetical study, so it’s very important that you should define it correctly. Because all the further steps depend on this. In this article, we discussed in detail what is Ho and Ha with examples and also understood how to write it with the help of problem statements.

In the end, we compared both types of hypothesis statements on the basis of different parameters. I hope this article helped you in understanding this important topic.

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