Chapter 10.3, Problem 91E

(a)

To determine

To decide whether you should use two-sample t procedure to perform inference about a difference in means or paired t procedures to perform inference about a mean difference, in each of the following given.

Answer to Problem 91E

The two sample t procedures.

Explanation of Solution

In this case, we need to use paired t procedures if the two samples contain the same subjects or if the subjects in one sample are related to the subjects in the other sample.

We need to use two sample t procedures if the subjects in the two sample are completely unrelated.

In this case, $50$ cars are randomly assigned to brand A or brand B thus the first sample is the cars assigned to brand A and the second sample is the cars assigned to brand B.

Since the cars were randomly assigned to one of the samples the cars in the two samples will be completely unrelated and thus it is appropriate to use the two sample t procedures.

(b)

To determine

To decide whether you should use two-sample t procedure to perform inference about a difference in means or paired t procedures to perform inference about a mean difference, in each of the following given.

Answer to Problem 91E

The paired t procedures.

Explanation of Solution

In this case, we need to use paired t procedures if the two samples contain the same subjects or if the subjects in one sample are related to the subjects in the other sample.

We need to use two sample t procedures if the subjects in the two sample are completely unrelated.

Each subject worked with music for one month and each subject worked without music for one month. The first sample is then the data for all subjects who worked with music for one month and the second sample is then the data for all subjects who worked without music for one month.

Since the two samples the same subjects we should use the paired t procedures.

(c)

To determine

To decide whether you should use two-sample t procedure to perform inference about a difference in means or paired t procedures to perform inference about a mean difference, in each of the following given.

Answer to Problem 91E

The paired t procedures.

Explanation of Solution

In this case, we need to use paired t procedures if the two samples contain the same subjects or if the subjects in one sample are related to the subjects in the other sample.

We need to use two sample t procedures if the subjects in the two sample are completely unrelated.

We have $40$ couples while the male and female partners were interviewed separately. The first sample then contains the male partners while the second sample contains the female partners.

Since all the subjects in the first sample are the male partners of a subject in the second sample, the subjects in the two samples are related and thus we should use the paired t procedures.