84. Suppose the population distribution is normal with known .

Let be such that 0   . For testing H0:
0 versus Ha: 0, consider the test that rejects H0 if either z  z or z  z , where the test statistic is Z
(X  0)/

(/n).

a. Show that P(type I error)
.

b. Derive an expression for
( ). [Hint: Express the test in the form “reject H0 if either x  c1 or  c2.”]

c. Let  0. For what values of (relative to ) will

(0 ) 
(0  )?