Refer to Exercise 8.99.

a. Find b for each of the following values of the population mean: 65.4, 63.4, 61.4, 59.4, and 57.4.

b. Plot each value of b you obtained in part a against its associated population mean. Show b on the vertical axis and m 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 m = 63.4.

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 m 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 m and the null-hypothesized mean m0, the value of

b, and the power.