10.65 Let m denote the mean diameter for bearings of a certain type. A test of H0: m 5 0.5 versus Ha: m Þ

0.5 will be based on a sample of n bearings. The diameter distribution is believed to be normal.

Determine the value of b in each of the following cases:

a. n 5 15, a 5 .05, s 5 0.02, m 5 0.52

b. n 5 15, a 5 .05, s 5 0.02, m 5 0.48

c. n 5 15, a 5 .01, s 5 0.02, m 5 0.52

d. n 5 15, a 5 .05, s 5 0.02, m 5 0.54

e. n 5 15, a 5 .05, s 5 0.04, m 5 0.54

f. n 5 20, a 5 .05, s 5 0.04, m 5 0.54 g. Is the way in which b changes as n,

a, s, and m vary consistent with your intuition? Explain.