## How to Support or Reject a Null Hypothesis (Using a P-Value)

Deciding to support or reject a null hypothesis in statistics can seem like an overwhelming task at first. The question will state that a researcher made a claim; your task is to decide whether the evidence supports the claim. If you have a P-value, or are asked to find a P-value, follow these instructions. If you do not have a P-Value, follow Reject/Support the Null Hypothesis instead.

Step 1: State the null hypothesis and the alternate hypothesis (“the claim”).
If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis.

Step 2: Find the critical value.
You should have already covered that topic by this point, but here is a how-to on finding the critical value for a left-tailed test as a reminder. You may need to find a right-tailed or two-tailed instead.

Step 3: Draw a normal distribution with your critical value. Shade in the appropriate area (i.e. for a right- or left-tailed test, shade in the tail).
Step 4: If you already have the population standard deviation, go straight to step 6. If you do not have the population standard deviation (i.e. you are presented with a list of data) go to step 5.

Step 5: Find the mean (X) and standard deviation (s) for the data.

Step 6:. Use the following formula to find the z-value. If you have the population standard deviation σ, use it instead of the sample population, s.

Click here if you want easy, step-by-step instructions for solving this formula.

If formulas confuse you, all this formula is asking you to do is:

1. Subtract the the null hypothesis mean  (μ–you figured this out in step 1) from the mean of the data ( from step 5). Set this number aside for a moment.
2. Divide the standard deviation (σ or s) by the square root of your sample size (the question either stated your sample size or you were given a certain amount n of data). For example, if thirty six children are in your sample and your standard deviation is 2, then 3/√36=0.5
3. Divide your result from step 1 by your result from step 2 (i.e. step 1/step2)

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Step 7: Find the P-Value by looking up your answer from step 6 in the z-table. Note: for a two-tailed test, you’ll need to double this amount to get the P-Value.

Step 8: Compare your answer from step 7 with the α value given in the question. If step 7 is less than α, reject the null hypothesis, otherwise do not reject it.

That’s it!

## 10 thoughts on “How to Support or Reject a Null Hypothesis (Using a P-Value)”

1. Stephanie

Jennifer,
Finding a test value (at least, in this case), is the same thing as finding a z-value–just follow the steps,
Stephanie

2. Sarah M. Joyner

The questions where you have to find the p-value and round to four decimals was confusing because when I thought I had the correct answer and compared it to the example problem that I was following somehow my rounding never matched up to theirs. It looked as if they were rounding up to the next whole number when looking at the z-table and I was just rounding the four decimals. Am I missing something?

3. Stephanie

Sarah, If you are referring to Mathzone, unfortunately there are often rounding errors in the system. Shoot me an email with a specific problem and your answer, and I’ll be able to tell whether it’s the system at fault. Stephanie

4. Vanessa DuBarry

I am having trouble finding the crtical values and when using them with two tailed tests. I also dont know when to use the greater than sign, or less than, or when it is equal to.. how do I know when to use the greater than or equal to sign. I read your examples but I dont seem to get it.

5. Stephanie

Vanessa,
It all depends on your hypothesis statement. For example, if you null hypothesis states that something is less than a certain amount, you would use the “less than” sign. Likewise, if your hypothesis is “greater than” you would use “greater than”.
Stephanie

6. Lauren Schultz

This is where i get lost. I have had to redo so many of the questions simply because i cannot figure out the proper wording on the accept/reject part.