A simple random sample of 50 students is taken from a local community college,which has a total of about 1500 students.Another simple random sample of 50 students is taken from a large state university,which has a total of approximately 20,000 students.The sampled students each answer a one-question survey which reads,"About how many MP3 songs do you own?" The sample average number of MP3 songs owned is calculated for the two sets of students.What can we conclude about the sampling variability in the sample average number of MP3 songs of the students sampled from the small community college as compared to that in the sample average of the students sampled from the large state university?
A)The sample mean from the small community college has less sampling variability than that from the large state university because there are fewer students at the small community college.
B)The sample mean from the small community college has more sampling variability than that from the large state university because there are more students at the large state university.
C)The sample mean from the small community college has about the same sampling variability as that from the large state university because the sample sizes are equal.
D)It is impossible to make any statements about the sampling variability of the two sample means because the students surveyed came from different schools.

Question

Quizplus · Accepted Answer

The sampling variability is primarily determined by the sample size, not the population size, as long as the population is sufficiently large. Since both samples are of equal size (50 students each), the sampling variability in the sample averages should be about the same, regardless of the total number of students at each institution.

A Simple Random Sample of 50 Students Is Taken from a Local