The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in our sample is anywhere from 6 to 12, we shall not reject the null hypothesis that p = 0.6; otherwise, we shall conclude that p does not equal 0.6.
a) Evaluate α assuming that p = 0.6. Use the binomial distribution.
b) Evaluate β for the alternatives p = 0.5 and p = 0.7.
c) Is this a good test procedure?
6. A fabric manufacturer believes that the proportion of orders for raw material arriving late is p = 0.6. If a random sample of 10 orders shows that 3 or fewer arrived late, the hypothesis that p = 0.6 should be rejected in favor of the alternative p < 0.6. Use the binomial distribution.
One- and Two-Sample Hypothesis Testing are investigated.