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. Let’s consider Exercise 7-45 on the Graded Naming Test. (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 score.)
a. Conduct step 2 of hypothesis testing for a one-tailed test—stating the null and research hypotheses in words and in symbols.
b. Conduct step 4 of hypothesis testing for a one-tailed test—determining the cutoff.
c. Conduct step 6 of hypothesis testing for a one-tailed test—making a decision.
d. Under which circumstance—a one-tailed or a two-tailed 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 now a bigger difference between the samples? Explain.