Chapter 21, Problem 25E

(a)

To determine

To explain is this a one-tailed or a two-tailed test and why.

Answer to Problem 25E

It is a one-tailed test.

Explanation of Solution

It is given in the question that a company is sued for the job discrimination because only $19\%$ of the newly hired candidates were minorities when $27\%$ of all applicants were minorities. Thus, from this context we can say that it is a one-tailed test because the company should not be sued if too many minorities were hired.

(b)

To determine

To explain what would a Type I error be.

Explanation of Solution

It is given in the question that a company is sued for the job discrimination because only $19\%$ of the newly hired candidates were minorities when $27\%$ of all applicants were minorities. Thus, in this context a Type I error would be defined as deciding that the company is discriminating when it actually is not.

(c)

To determine

To explain what would a Type II error be.

Explanation of Solution

It is given in the question that a company is sued for the job discrimination because only $19\%$ of the newly hired candidates were minorities when $27\%$ of all applicants were minorities. Thus, in this context a Type II error would mean that deciding that the company is not discriminating when it actually is.

(d)

To determine

To explain what is meant by the power of the test.

Explanation of Solution

It is given in the question that a company is sued for the job discrimination because only $19\%$ of the newly hired candidates were minorities when $27\%$ of all applicants were minorities. Thus, in this context the power of the test means that the probability of correctly detecting discrimination when it actually exists.

(e)

To determine

To explain how will this affect the power of the test.

Answer to Problem 25E

It will increase.

Explanation of Solution

It is given in the question that a company is sued for the job discrimination because only $19\%$ of the newly hired candidates were minorities when $27\%$ of all applicants were minorities.Thus, in this context the power of test will be affected as it will increase the power because power is $1-\beta$ and $\beta$ decreases as $\alpha$ increases. Therefore, a lower $\beta$ means higher power.

(f)

To determine

To explain is the power of the test higher than, lower than or the same as it would be if it were based on $87$ hires.

Answer to Problem 25E

The power of the test lower than as it would be if it were based on $87$ hires.

Explanation of Solution

It is given in the question that a company is sued for the job discrimination because only $19\%$ of the newly hired candidates were minorities when $27\%$ of all applicants were minorities. Thus, we can say that the power of the test lower than as it would be if it were based on $87$ hires because the sample size will be smaller and thus it will also be lower.