Let m denote the true average lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test of H0: m 10 versus Ha:

m  10 will be based on a sample of size 36. Suppose that s is known to be 0.6, from which sx 5 .1. The appropriate test statistic is then z 5 x 2 10 0.1

a. What is a for the test procedure that rejects H0 if z  1.28?

b. If the test procedure of Part

(a) is used, calculate b when m 9.8, and interpret this error probability.

c. Without doing any calculation, explain how b when 9.5 compares to b when m 9.8. Then check your assertion by computing b when m 9.5.

d. What is the power of the test when m 9.8? when m 9.5?