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) Yes, since the central limit theorem works whenever proportions are used
B) Yes, since $n \geq 30$
C) Yes, since both $n p$ and $n q$ are greater than or equal to 15
D) $\mathrm { No }$

Question

Quizplus · Accepted Answer

The sample size is large enough if both $n p$ and $n q$ are greater than or equal to 15, where $p$ is the proportion of interest (0.20) and $q = 1 - p$. Here, $n p = 108 \times 0.20 = 21.6$ and $n q = 108 \times 0.80 = 86.4$, both of which are greater than 15.

A Small Private College Is Interested in Determining the Percentage 20%20 \%20%

A Small Private College Is Interested in Determining the Percentage $20 \%$