Chapter 9.2, Problem 44E

a)

To determine

Interpret Type I error and a Type II error in given situation.

Explanation of Solution

Given:Let “ p” be the proportion of subjects experience nausea.

p = 0.10

n = total sample size = 300

Type I error : Incorrectly rejecting a true null hypothesis. It is also known as false positive.

Null hypothesis is 10% of patients who take the new drug will experience nausea.

Alternate hypothesis is less than 10% of patients who take the new drug will experience nausea.

Type I error here is concluding that less than 10% of patients who take the new drug will experience nausea but it is actually false. The consequence of this error may lead to patient death.

Type II error: Fail to reject a false null hypothesis. It is also known as false negative.

Type II error here is concluding that it is not less than 10% of patients who take the new drug will experience nausea when it is actually less than 10%. The consequence of this error is not serious as action will be taken to reduce the patient’s discomfort.

b)

To determine

Explain the given statement “The test has a power of 0.54 to detect that p = 0.07.”

Explanation of Solution

Power is the probability that the test rejects the null hypothesis, when alternate hypothesis is true. It is nothing but probability of avoiding false negative or Type II error.

Here we have the power of the test as 0.54 to detect that p = 0.07. This indicates that the probability of rejecting null hypothesis when p = 0.07 is 0.54.

c)

To determine

The two ways to increase the power of test.

Explanation of Solution

Power is the probability that the test rejects the null hypothesis, when alternate hypothesis is true. It is nothing but probability of avoiding false negative or Type II error.

To maximize the power of the test, we have to choose a large sample size or we need to choose a higher value of level of significance a.