Question

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or

type II error for the test.


A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets

have a standard deviation of 3. 3 mg. Identify the type II error for the test.


A. Reject the claim that the standard deviation is 3. 3 mg when it is actually equal to 3. 3 mg.


B. Fail to reject the claim that the standard deviation is 3. 3 mg when the standard deviation is actually

different from 3. 3 mg.


C. Fail to reject the claim that the standard deviation is 3. 3 mg when the standard deviation is actually

equal to 3. 3 mg.


D. Reject the claim that the standard deviation is 3. 3 mg when it is actually different from 3. 3 mg

Answer 1

Answer: The correct answer is:

C. Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is actually equal to 3.3 mg.

A Type II error occurs when the null hypothesis (the claim in this case) is true, but we fail to reject it based on the sample evidence. In this context, it means that the manufacturer's claim that the standard deviation is 3.3 mg is actually true (null hypothesis is true), but we fail to recognize it and do not reject the claim based on the data from the hypothesis test.

In other words, we mistakenly conclude that the standard deviation is different from 3.3 mg (as in option B or D), when it is not, and we fail to accept the manufacturer's claim (as in option C).