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 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.
If formulas confuse you, all this formula is asking you to do is:
- 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.
- 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
- Divide your result from step 1 by your result from step 2 (i.e. step 1/step2)
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.