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

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

A:

Power of test = Probability of true-positive

.......................= 1 - probability of false-negative

Therefore,

The power of the test = The probability of arresting a driver who is drunk.

Or

The power of the test = 1 - The probability of not arresting a driver who is drunk (type II error).

Q: 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:

Lowering the significance level from 0.05 to 0.01 would amplify the false-negative results (type II) error, lower the power of the test, thus makes it harder to reject the false null hypothesis.