# AP Statistics : How to do tests of significance for a difference between two means

## Example Questions

### Example Question #1 : How To Do Tests Of Significance For A Difference Between Two Means

Suppose you conduct a paired -test to assess whether two group means significantly differ and find a -score of 1.645. At what alpha level would this cause you to reject the null?

Possible Answers:

Correct answer:

Explanation:

The critical value for a -test with alpha set to 0.10 is 1.645.

### Example Question #6 : Significance

Bob wants to statistically determine if the mean height of middle school boys is greater than the mean height of middle school girls. He wants to use a significance level of  What must be true for him to reject . is known.

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to use a 2-sample z test because there are 2 samples, boys and girls. The population standard deviation, , is known, so we can assume a standard distribution for each sample.

Step 2: This is a one-sided z test because the questions asks if the mean height of boys is greater than the mean height of girls.

Step 3: significance level, or alpha, is . This means we need a p-value less than  in order to reject the null hypothesis . A z-score greater than would ensure a p-value less than .