Question

Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice. ${}^{+3}$

(a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which page in each pair got Ration and which got Ration B.

(b) A random sample of college professors is taken.

We wish to compare the average salaries of male and female teachers.

(c) To test the effects of a new fertilizer, plots are treated with the new fertilizer, and plots are treated with another fertilizer. A computer's random number generator is used to determine which plots get which fertilizer.

Short answer

a) Paired t procedures

b) Two-sample t procedures

c)Two-sample t procedures

Step-by-step solution

Part (a) Step 1: Given Information

To determine whether paired t-test or two-sample t-test should be used to conduct inference on the basis of the information provided.

Part (a) Step 2: Explanation

If a value in one sample has an associating value in another, paired $t$procedures are employed; otherwise, two-sample $t$techniques are utilized.

$t$operations that are paired

Because every participant in another sample has a littermate,

Part (b) Step 1: Given Information

To determine whether paired t-test or two-sample t-test should be used to conduct inference on the basis of the information provided.

Part (b) Step 2: Explanation

When a value in one sample corresponds to a value in the other, paired $t$methods are employed; otherwise, two-sample $t$procedures are utilized.

$t$operations with two samples

Because each sample has a large number of individuals,

Part (c) Step 1: Given Information

To determine whether paired t-test or two-sample t-test should be used to conduct inference on the basis of the information provided.

Part (c) Step 2: Explanation

If a value in one sample has a similar value in the other sample, paired $t$procedures are employed; otherwise, two-sample $t$procedures are utilized.

$t$operations with two samples

Because each sample has a variety of people,