Chapters 20-21 Summative Assessment

Question

A police officer uses a breathalyzer to test the blood alcohol content of drivers suspected of a DUI. The driver will be arrested if the officer believes that the driver is drunk, according to the results of the breathalyzer. The hypotheses can be stated as follows:

H₀ : The driver is not drunk.

H_a : The driver is drunk.

Which of the following best describes the power of the test?

a	The probability of arresting a driver who is drunk.
b	The probability of not arresting a driver who is not drunk.
c	The probability of not arresting a driver who is drunk.
d	The probability of arresting a driver who is not drunk.
e	The probability that the breathalyzer is working correctly.

A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true?

a

Neither the probability of a Type II error nor the power of the test would change.

b

The probability of a Type II error would decrease and the power of the test would increase.

c

Both the probability of a Type II error and the power of the test would increase.

d

The probability of a Type II error would increase and the power of the test would decrease.

e

Both the probability of a Type II error and the power of the test would decrease.

Answer 1

Answer to the first question:

The power of a test is the probability of correctly rejecting the null hypothesis when it is false, meaning it is the probability of detecting a true effect. In this case, it refers to the probability of arresting a driver who is actually drunk.

Correct answer: (a) The probability of arresting a driver who is drunk.

Answer to the second question:

The significance level (α) is the probability of making a Type I error (rejecting the null hypothesis when it is actually true). When the significance level is decreased from 0.05 to 0.01, the test becomes more conservative, reducing the likelihood of Type I errors but increasing the probability of a Type II error (failing to reject the null when it is false). Since power is 1− (Type II error probability), a higher probability of a Type II error leads to lower power.

Correct answer: (d) The probability of a Type II error would increase and the power of the test would decrease.