The proportion of adults living in a small town who are college graduates is estimated to be = 0.8. To test this hypothesis a random sample of 12 adults is selected. The fail to reject zone is defined as 8 x 10, where x is the number of college graduates in the sample.

Calculate (probability of type I error) assuming that = 0.8

Assume that instead of using a sample of 12, you get a fresh sample of 144 adults. This time, the fail to reject zone is defined as 100 x 120. Calculate (probability of type II error) and the power of the test for the alternative = 0.6.