Refer to Exercise 8.101.

a. Find b for each of the following values of the population mean: 49, 47, 45, 43, and 41.

b. Plot each value of b you obtained in part a against its associated population mean. Show b on the vertical axis and µ on the horizontal axis. Draw a curve through the five points on your graph.

c. Use your graph from part b to find the approximate probability that the hypothesis test will lead to a Type II error when µ = 48.

d. Convert each of the b values you calculated in part a to the power of the test at the specified value of m. Plot the power on the vertical axis against µ on the horizontal axis. Compare the graph of part b with the power curve you plotted here.

e. Examine the graphs of parts b and d. Explain what they reveal about the relationships among the distance between the true mean µ and the null-hypothesized mean m0, the value of b, and the power.