Again consider the automobile parts supplier situation. Remember that a problem- solving team will be assigned to rectify the process producing the cylindrical engine parts if the null hypothesis H0: μ = 3 is rejected in favor of Ha: μ = 3. In this exercise we calculate probabilities of various Type II errors in the context of this situation.

a. Suppose that the parts supplier’s hypothesis test is based on a sample of n 100 diameters and that s equals .023. If the parts supplier sets α = .05, calculate the probability of a Type II error for each of the following alternative values of μ: 2.990, 2.995, 3.005, 3.010.

b. If we want both the probabilities of making a Type II error when m equals 2.995 and when m equals 3.005 to be very small, is the parts supplier’s hypothesis test adequate? Explain why or why not. If not, and if we wish to maintain the value of α at .05, what must be done?

c. Plot the power of the test versus the alternative values of m in part a. What happens to the power of the test as the alternative value of μ moves away from 3?