Chapter 21, Problem 20E

(a)

To determine

To explain what are the null and alternative hypotheses.

Explanation of Solution

It is given in the question that testing for Alzheimer’s disease can be a long and expensive process consisting of lengthy tests and medical diagnosis. And a group of researchers devised a seven-minute test to serve as a quick screen for the disease for use in the general population of senior citizen. Thus, the null hypothesis states that a person is healthy. The alternative hypothesis states that the opposite of the null hypothesis. The alternative hypothesis states that a person has Alzheimer's disease.

(b)

To determine

To explain what would a Type I error mean.

Explanation of Solution

It is given in the question that testing for Alzheimer’s disease can be a long and expensive process consisting of lengthy tests and medical diagnosis. And a group of researchers devised a seven-minute test to serve as a quick screen for the disease for use in the general population of senior citizen. Thus, the null hypothesis states that a person is healthy. The alternative hypothesis states that the opposite of the null hypothesis. The alternative hypothesis states that a person has Alzheimer's disease. So, the Type I error means that when you decide a person has Alzheimer's when they actually do not.

(c)

To determine

To explain what would a Type II error mean.

Explanation of Solution

It is given in the question that testing for Alzheimer’s disease can be a long and expensive process consisting of lengthy tests and medical diagnosis. And a group of researchers devised a seven-minute test to serve as a quick screen for the disease for use in the general population of senior citizen. Thus, the null hypothesis states that a person is healthy. The alternative hypothesis states that the opposite of the null hypothesis. The alternative hypothesis states that a person has Alzheimer's disease. So, the Type I error means that whenyou fail to diagnose a person with Alzheimer's when the person actually has it.

(d)

To determine

To explain which is worse here, Type I or Type II error.

Answer to Problem 20E

Type II error is worse.

Explanation of Solution

It is given in the question that testing for Alzheimer’s disease can be a long and expensive process consisting of lengthy tests and medical diagnosis. And a group of researchers devised a seven-minute test to serve as a quick screen for the disease for use in the general population of senior citizen. Thus, the null hypothesis states that a person is healthy. The alternative hypothesis states that the opposite of the null hypothesis. The alternative hypothesis states that a person has Alzheimer's disease. Now, we know that,

In Type I: It requires more testing which leads to a loss of time and money.

In Type II: The person did not receive the treatment that they needed.

therefore, a Type II error would be much worse in this case.

(e)

To determine

To explain what is the power of the test.

Answer to Problem 20E

  $0.92$ .

Explanation of Solution

It is given in the question that testing for Alzheimer’s disease can be a long and expensive process consisting of lengthy tests and medical diagnosis. And a group of researchers devised a seven-minute test to serve as a quick screen for the disease for use in the general population of senior citizen. Thus, the null hypothesis states that a person is healthy. The alternative hypothesis states that the opposite of the null hypothesis. The alternative hypothesis states that a person has Alzheimer's disease. So, the power of test is then as:

  $\begin{array}{l}P=1-P(\text{Type II error})\\ =1-0.08\\ =0.92\end{array}$