What happens to the power of the test as the alternative value of μ moves away from 60?
The power curve for a statistical test is a plot of the power = 1 − β on the vertical axis versus values of μ that make the null hypothesis false on the horizontal axis. Plot the power curve for Consolidated Power’s test of H0: μ ≤ 60 versus Ha: μ > 60 by plotting power = 1 − β for each of the alternative values of μ in part a. What happens to the power of the test as the alternative value of μ moves away from 60?
9.81 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 σ equals .023. If the parts supplier sets α = .05, calculate the probability of a TypeII error for each of the following alternative values of μ: 2.990, 2.995, 3.005, 3.010.
b If we want the probabilities of making a Type II error when μ equals 2.995 and when μ equals 3.005 to both 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?