When to Use p-value, When to Use Level of Significance

When you do a hypothesis test, you use a sample to come up with a test statistic (z-value). Then you use the z-value to come up with a p-value, where the p-value is the area of the “tail(s)” involved.

Now the book says that you decide the result of the hypothesis test based on the size of the p-value (page 438). The smaller the p-value the more evidence against the null hypothesis you have. This is true if you are not given a level of significance (ie no ).

But what happens if the problem says to use 1% or 5% level of significance ( or ) ?

This just means that when you are done you compare the p-value to this to decide whether you reject the null hypothesis or not.

If , then you reject the null hypothesis and say the result is “significant”.

If , then you say there is not enough evidence to reject the null hypothesis and say the result is “not significant”.

Example (Using a level of significance in hypothesis test):

As an example suppose you are using a level of significance and your p-value is . Then reject the null hypothesis and say the result is significant.

Or suppose your level of significance is and your p-value is . Then you do not have enough evidence to reject the null hypothesis and say the result is not significant.

So the upshot is compare the p-value to the level of significance () to decide whether to reject when you have a level of significance. If the problem doesn’t give a level of significance, then decide your conclusion by using the size of the p-value and the table on p. 438 of our book.