Chapter 21, Problem 19E

(a)

To determine

To explain what will their hypotheses be.

Explanation of Solution

It is given in the question that the U.S. census reported that $68.9\%$ of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. Thus, the null hypothesis states that the level of home ownership remains the same. And the alternative hypothesis states the opposite of the null hypothesis. So, the alternative hypothesis states that the level of home ownership rises.

(b)

To determine

To explain what would a Type I error be.

Explanation of Solution

It is given in the question that the U.S. census reported that $68.9\%$ of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. Thus, the null hypothesis states that the level of home ownership remains the same. And the alternative hypothesis states the opposite of the null hypothesis. So, the alternative hypothesis states that the level of home ownership rises. Thus, we can say that the Type I error would be that the city concludes that home ownership is on the rise, but the taxes don't actually help.

(c)

To determine

To explain what would a Type II error be.

Explanation of Solution

It is given in the question that the U.S. census reported that $68.9\%$ of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. Thus, the null hypothesis states that the level of home ownership remains the same. And the alternative hypothesis states the opposite of the null hypothesis. So, the alternative hypothesis states that the level of home ownership rises. Thus, we can say that the Type II error would be that thecity abandons the tax breaks, but they are in reality helping.

(d)

To determine

To explain for each type of error tell who would be harmed.

Explanation of Solution

It is given in the question that the U.S. census reported that $68.9\%$ of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. Thus, the null hypothesis states that the level of home ownership remains the same. And the alternative hypothesis states the opposite of the null hypothesis. So, the alternative hypothesis states that the level of home ownership rises. Thus, for each type of error,

In Type I error: The city foregoes tax revenue would be harmed.

And in Type II error: Help is withdrawn from those who may otherwise have been able to afford a home.

(e)

To determine

To explain what would the power of the test represent in this context.

Explanation of Solution

It is given in the question that the U.S. census reported that $68.9\%$ of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. Thus, the null hypothesis states that the level of home ownership remains the same. And the alternative hypothesis states the opposite of the null hypothesis. So, the alternative hypothesis states that the level of home ownership rises. Thus, the power of test represent in this context that the power of the test is the city's ability to correctly detect an increase in home ownership.