The proportion of adults living in a small town who are college graduates is estimated to be p=0.4. To test this hypothesis, a random sample of 10 adults is selected. If the number of college graduates in the sample is anywhere from 3 to 5 , we shall not reject the null hypothesis that p=0.4; otherwise, we shall conclude that p=0.4. Complete parts (a) through (c) below.
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(a) Evaluate α assuming that p=0.4. Use the binomial distribution.
α= (Round to four decimal places as needed.)
(b) Evaluate β for the aiternatives p=0.3 and p=0.5.
For the alternative p=0.3,β= (Round to four decimal places as needed.)