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. ${}^{42}$

(a) To test the wear characteristics of two tire brands, A and B, each brand of tire is randomly assigned to 50 cards of the same make and model.

(b) To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

(c) A study was designed to compare the effectiveness of two weight-reducing diets. Fifty obese women who volunteered to participate were randomly assigned into two equal-sized groups. One group used Diet \(A\) and the other used Diet B. The weight of each woman was measured before the assigned diet and

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

If each value in one sample has an associating value in the other sample, paired $t$techniques are used; otherwise, two-sample $t$procedures are used.

$t$operations with two samples

Because each sample contains a different set of tyres.

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

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

$t$operations that are paired.

Because every subject is represented in both samples.

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

If a value in one sample has a corresponding value in the other, we utilize paired $t$methods; otherwise, we use two-sample $t$procedures.

$t$operations with two samples

Because each sample has a large number of individuals,