The proportion of adults living in Tempe, Arizona, who are college graduates is estimated to be p = 0.4. To test this hypothesis, a random sample of 15 Tempe adults is selected. If the number of college graduates is between 4 and 8, the hypothesis will be accepted; otherwise, we will conclude that.
(a) Find the type I error probability for this procedure, assuming that p = 0.4.
(b) Find the probability of committing a type II error if the true proportion is really p = 0.2.