9.59      A test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points. A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points. (a) Write the hypotheses for a left-tailed test of the mean.

(b) Explain the consequences of a Type I error in this context.

9.60      Telemarketers use a predictive dialing system to decide whether a person actually answers a call (as opposed to an answering machine). If so, the call is routed to a telemarketer. If no telemarketer is free, the software must automatically hang up the phone within two seconds, to comply with FAA regulations against tying up the line. The Touchstar company says that its new system is smart enough to hang up on no more than 2 percent of the answered calls. Write the hypotheses for a right-tailed test, using Touchstar’s claim about the proportion as the null hypothesis. (See The New York Times, Nov. 15, 2007, p. C12.)

9.61      If the true mean is 50 and we reject the hypothesis that μ = 50, what is the probability of Type II error? Hint: This is a trick question.

9.62      If we fail to reject the null hypothesis that π = .50 even though the true proportion is .60, what is the probability of Type I error? Hint: This is a trick question.