The proportion of adults living in a small town who are college graduates is estimated to be p = 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.

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The proportion of adults living in a small town who are college graduates is estimated to be p =
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.
(a) Calculate a (probability of type I error) assuming that p = 0.8.
(b) 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 ß (probability of type II error) and
the power of the test for the alternative p = 0.6.
Transcribed Image Text:The proportion of adults living in a small town who are college graduates is estimated to be p = 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. (a) Calculate a (probability of type I error) assuming that p = 0.8. (b) 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 ß (probability of type II error) and the power of the test for the alternative p = 0.6.
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