Question

Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits.

Select the correct answer below:

A. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits.
B. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits.
C. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits.
D. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits.

Answer 1

The Type II error is when the building inspector thinks that more than 15% of the structures in the county were built without permits, when in fact, at most 15% of the structures were built without permits.

Step-by-step explanation:

The Type II error is when the building inspector thinks that more than 15% of the structures in the county were built without permits, when in fact, at most 15% of the structures were built without permits.

It means that the building inspector fails to reject the null hypothesis (H0) that no more than 15% of structures were built without permits, even though it is actually false. This is represented by option C in the question.

Answer 2

D. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits.

Step-by-step explanation:

A type II error is defined "as the probability of incorrectly retaining the null hypothesis, when in fact it is not applicable to the entire population"

Based on the null hypothesis given:

H0: a building inspector claims that no more than 15% of structures in the county were built without permits.

So then the alternative hypothesis, by the complement rule would be given by:

Ha: a building inspector claims that more than 15% of structures in the county were built without permits.

Based on this we can conclude that the correct option on this case would be:

D. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits.

And the reason why is because we are retaining or FAIL to reject the null hypothesis when actually is FALSE.