Let denote a random sample from a normal population distribution with a known value of s.

a. For testing the hypotheses versus

(where m0 is a fixed number), show that the test with test statistic and rejection region has significance level .01.

b. Suppose the procedure of part

(a) is used to test versus . If , and , what is the probability of committing a type I error when ? When ? 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.