Statistics How To

How to State the Null Hypothesis in Statistics

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How to State the Null Hypothesis from a Word Problem

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis. Breaking your problem into a few small steps makes these problems much easier to handle.

How to State the Null Hypothesis

Sample Problem: A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3 times), their recovery period will be longer. Average recovery times for knee surgery patients is 8.2 weeks. 

how to state the null hypothesis

Hypothesis testing is vital to test patient outcomes.


Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is “I expect the average recovery period to be greater than 8.2 weeks.”

Step 2: Convert the hypothesis to math. Remember that the average is sometimes written as  μ.

H1: μ > 8.2

Broken down into (somewhat) English, that’s H1 (The  hypothesis): μ (the average) > (is greater than) 8.2

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

H0: μ ≤ 8.2

Broken down again into English, that’s H0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

How to State the Null Hypothesis: Part Two

But what if the researcher doesn’t have any idea what will happen?

Sample Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks. 

Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

H0: μ = 8.2

Broken down into English, that’s H0 (The null hypothesis): μ (the average) =(is equal to) 8.2

Step 2: Figure out the alternate hypothesis. The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

H1: μ ≠ 8.2

In English again, that’s H1 (The  alternate hypothesis): μ (the average) ≠ (is not equal to) 8.2

That’s How to State the Null Hypothesis!

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12 thoughts on “How to State the Null Hypothesis in Statistics

  1. Angie Widdows

    This was a good example. It is the next step that I often have problems with. This example helps because it (like others) lists out the meaning of the symbols. Very helpful

  2. Lisa Barcomb

    Understanding the null hypothesis is much easier now because when you go to convert it to math it makes a lot more sense in figuring out the formulas that you are suppose to be working with. I think I put more into these problems then I really need to.

  3. Vanessa DuBarry

    This example really helped me, because it explains how to put it into english, and at first it was kind of hard knowing what sign goes were, but this really helped.

  4. Donna Allen

    At first, I was a little intimidated by this. But, after going over your instructions, it seems fairly easy. Thanks!

  5. Bill Bryan

    I was starting to get that sinking feeling until I read this, love the matter of fact approch to discribing the steps.