Chapter 10.3, Problem 92E

(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 92E

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.

All pigs in each pair were littermates. One pig in each pair received diet A and the other pig in each pair received diet B. the first sample then contains all pigs received diet A and the second sample then contains all pigs received diet B.

Since all the pigs in the first sample are the littermates of a pig in the second sample then the pig in the two samples are related and thus we should use the paired 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 92E

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.

Separate random samples were taken for the male college professors and female college professors thus the first sample is the random sample of male college professors and the second sample is the random sample of female college professors.

Since the two samples are separate random samples the professors in the two samples are completely unrelated and thus we should use the two-sample 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 92E

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.

  $100$ plots are treated with the new fertilizers and $100$ plots are treated with the another fertilizers thus the first sample is the $100$ plots are treated with the new fertilizers and the second sample is the $100$ plots are treated with the another fertilizers.

Since the plots were randomly assigned a fertilizers the plots in the two sample will be completely unrelated and thus it is appropriate to use the two-sample t procedures.