10.63 The amount of shaft wear after a fixed mileage was determined for each of seven randomly selected internal combustion engines, resulting in a mean of 0.0372 inch and a standard deviation of 0.0125 inch.

a. Assuming that the distribution of shaft wear is normal, Use a 5 .05 to test the hypotheses H0: m 5 .035 versus Ha: m . .035.

b. Using s 5 0.0125, a 5 .05, and Appendix Table 5, what is the approximate value of

b, the probability of a Type II error, when m 5 .04?

(Hint: See Example 10.19.)

c. What is the approximate power of the test when m 5 .04 and a 5 .05?