(Solution) - The proportion of adults living in Tempe Arizona who are -(2025 Original AI-Free Solution)

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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.