13. Let X1, . . . , Xn denote a random sample from a normal population distribution with a known value of s.

a. For testing the hypotheses H0: m  m0 versus Ha:

m m0 (where m0 is a xed number), show that the test with test statistic and rejection region has signi cance level .01.

b. Suppose the procedure of part

(a) is used to test H0: m m0 versus Ha: m m0. If m0  100, n 

25, and s  5, what is the probability of committing a type I error when m  99? When m 

98? In general, what can be said about the probability of a type I error when the actual value of m is less than m0? Verify your assertion.