A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. The college decided to take a random sample of 108 of their current students to use in the analysis. Is the sample size of n = 108 large enough to use this inferential procedure?
A) No
B) Yes, since n ≥ 30
C) Yes, since both np and nq are greater than or equal to 15
D) Yes, since the central limit theorem works whenever proportions are used

Question

Quizplus · Accepted Answer

The sample size is large enough if both np and nq are greater than or equal to 15, where p is the proportion of interest (0.20 in this case) and q is 1-p. Here, np = 108 * 0.20 = 21.6 and nq = 108 * 0.80 = 86.4, both of which are greater than 15.

A Small Private College Is Interested in Determining the Percentage