Chapter 10.2, Problem 3E

Refer to Exercise 10.2.

1. a Find the rejection region of the form {y ≤ c} so that α ≈ .01.
2. b For the rejection region in part (a), find β when p = .6.
3. c For the rejection region in part (a), find β when p = .4.

10.2 An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people suffering from insomnia. After examining the dosage, we feel that her claims regarding the effectiveness of the dosage are inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs and we observe Y, the number for whom the drug dose induces sleep. We wish to test the hypothesis H₀: p = .8 versus the alternative. H_a: p < .8. Assume that the rejection region {y ≤ 12} is used.

1. a In terms of this problem, what is a type I error?
2. b Find α.
3. c In terms of this problem, what is a type II error?
4. d Find β when p = .6.
5. e Find β when p = .4.