Chapter 8.1, Problem 34BB

Calculating Power Consider a hypothesis test of the claim that the Ericsson method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p > 0.5. Assume that a significance level of α = 0.05 is used, and the sample is a simple random sample of size n = 64.

a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when it is false. (Hint: With a 0.05 significance level, the critical value is z = 1.645, so any test statistic in the right tail of the accompanying top graph is in the rejection region where the claim is supported. Find the sample proportion $\hat{p}$ in the top graph, and use it to find the power shown in the bottom graph.)

b. Explain why the green-shaded region of the bottom graph represents the power of the test.