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.

Answer 1

Complete 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:

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:

Type II error means not rejecting the null hypothesis while, in the actual sense, the null hypothesis is false.

In this question, the null hypothesis states that:

$H_0$: a building inspector claims that no more than 15% of structures in the county were built without permits.

Therefore using the complement or alternative rule, we will have a hypothesis :

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

Using this alternative hypothesis we can conclude that the answer is "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", because we are not rejecting the null hypothesis when it is false considering a type II error.