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

Hello!

Statistical power indicates the probability that we will detect an effect if there is a real effect to be found (i.e., a true positive). Type II error indicates the probability that we will not detect an effect if there is a real effect to be found (i.e., a false negative).

For the first part of your question, that's answer A.

For the second part of your question, if we increase the significance level, we're less likely to capture a true positive. This means the statistical power decreases. We're more likely to get a false negative. This means the Type II error increases. That's answer D.

It might be helpful to look for a table summarizing Type I and Type II error (e.g., there's a nice one on Scribbr), which can be a helpful tool for these kinds of questions.

Best of luck!