An experimenter has prepared a drug dosage level that she

Chapter 10, Problem 2E

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QUESTION:

Problem 2E

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, Ha : p < .8. Assume that the rejection region {y ≤ 12} is used.

a In terms of this problem, what is a type I error?

b Find α.

c In terms of this problem, what is a type II error?

d Find β when p = .6.

e Find β when p = .4.

Questions & Answers

QUESTION:

Problem 2E

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, Ha : p < .8. Assume that the rejection region {y ≤ 12} is used.

a In terms of this problem, what is a type I error?

b Find α.

c In terms of this problem, what is a type II error?

d Find β when p = .6.

e Find β when p = .4.

ANSWER:

Step 1 of 2

It is given that  and   .

The rejection region .

a.)  To find the type I error.

The type I error occurs, Rejecting  when  is true.

Here, It is claimed that the drug is worse when in fact  of people suffering from insomnia are able to sleep after taking the drug.

b.)  To find .

Therefore, .

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