Question

Descriptions of three studies are given. In each of the studies, the two populations of interest are students majoring in science at a particular university and students majoring in liberal arts at this university. For each of these studies, indicate whether the samples are independently selected or paired. Study 1: To determine if there is evidence that the mean number of hours spent studying per week differs for the two populations, a random sample of 100 science majors and a random sample of 75 liberal arts majors are selected. Study 2: To determine if the mean amount of money spent on textbooks differs for the two populations, a random sample of science majors is selected. Each student in this sample is asked how many units he or she is enrolled in for the current semester. For each of these science majors, a liberal arts major who is taking the same number of units is identified and included in the sample of liberal arts majors. Study 3: To determine if the mean amount of time spent using the campus library differs for the two populations, a random sample of science majors is selected. A separate random sample of the same size is selected from the population of liberal arts majors.

Short answer

Study 1 and Study 3 use independently selected samples, while Study 2 uses paired samples.

Step-by-step solution

Identify sampling for Study 1

In Study 1, a random sample of science majors and a random sample of liberal arts majors are independently chosen, without any specified connection or pairing between individuals in the two groups. Hence, this implies that the samples are independently selected.

Identify sampling for Study 2

In Study 2, a random sample of science majors is selected. Moreover, each science major is paired with a liberal arts major who is enrolled in the same number of units. This process establishes a direct relationship between each individual in the two groups, therefore, it implies that the samples are paired.

Identify sampling for Study 3

In Study 3, random samples of science majors and liberal arts majors are chosen, but no connection is made between individuals in the two groups. Consequently, the samples are independently selected.