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One- and Two-Sample Hypothesis Testing

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.

a) Find the probability of committing a type I error if the true proportion is p = 0.6.
b) Find the probability of committing a type II error for the alternatives p = 0.3, p = 0.4, and p = 0.5.

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One- and Two-Sample Hypothesis Testing are investigated.

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