# Researchers often use z tests to compare their samples to

a. Conduct all six steps of a z test. Be sure to label all six steps.

b. Some words on the GNT are more commonly used in England. For example, a mitre, the headpiece worn by bishops, is worn by the archbishop of Canterbury in public ceremonies in England. No Canadian participant correctly responded to this item, whereas 55% of English adults correctly responded. Explain why we should be cautious about applying norms to people different from those on whom the test was normed.

c. When we conduct a one-tailed test instead of a two-tailed test, there are small changes in steps 2 and 4 of hypothesis testing. (Note: For this example, assume that those from populations other than the one on which it was normed will score lower, on average. That is, hypothesize that the Canadians will have a lower mean.) Conduct steps 2, 4, and 6 of hypothesis testing for a one-tailed test.

d. Under which circumstance—a one-tailed or a twotailed test—is it easier to reject the null hypothesis? Explain.

e. If it becomes easier to reject the null hypothesis under one type of test (one-tailed versus two tailed), does this mean that there is a bigger difference between the groups with a one tailed test than with a two-tailed test? Explain.

f. When we change the p level that we use as a cutoff, there is a small change in step 4 of hypothesis testing. Although 0.05 is the most commonly used p level, other values, such as 0.01, are often used. For this example, conduct steps 4 and 6 of hypothesis testing for a two-tailed test and p level of 0.01, determining the cutoff and drawing the curve.

g. With which p level—0.05 or 0.01—is it easiest to reject the null hypothesis? Explain.

h. If it is easier to reject the null hypothesis with certain p levels, does this mean that there is a bigger difference between the samples with one p level versus the other p level? Explain.