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

a. For testing the hypotheses H0:
0 versus Ha:

0 (where 0 is a fixed number), show that the test with test statistic X and rejection region x

 0 2.33/n has significance level .01.

b. Suppose the procedure of part

(a) is used to test H0: 

0 versus Ha: 0. If 0
100, n
25, and
5, what is the probability of committing a type I error when

99? When
98? In general, what can be said about the probability of a type I error when the actual value of is less than 0? Verify your assertion.