In an exercise in Chapter 7, we asked you to conduct a z test to ascertain whether the Graded Naming Test (GNT) scores for Canadian participants differed from the GNT norms based on adults in England. We also used these data in the How It Works section of this chapter. The mean for a sample of 30 adults in Canada was 17.5. The normative mean for adults in England is 20.4, and we assumed a population standard deviation of 3.2. With 30 participants, the z statistic was −4.97, and we were able to reject the null hypothesis.

a. Calculate the test statistic for 3 participants. How does the test statistic change compared to when N of 30 was used? Conduct step 6 of hypothesis testing. Does your conclusion change? If so, does this mean that the actual difference between groups changed? Explain.

b. Conduct steps 3, 5, and 6 for 100 participants. How does the test statistic change?

c. Conduct steps 3, 5, and 6 for 20,000 participants. How does the test statistic change?

d. What is the effect of sample size on the test statistic?

e. As the test statistic changes, has the underlying difference between groups changed? Why might this present a problem for hypothesis testing?