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 both np and nq are greater than or equal to 15
C) Yes, since the central limit theorem works whenever proportions are used
D) Yes, since $\mathrm { n } \geq 30$

Question

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 both np and nq are greater than or equal to 15
C) Yes, since the central limit theorem works whenever proportions are used
D) Yes, since $\mathrm { n } \geq 30$

Quizplus · Accepted Answer

The sample size is considered large enough for inferential procedures when both np and nq are greater than or equal to 15, where n is the sample size, p is the probability of success, and q is the probability of failure (q = 1 - p). Assuming the college wants to test if less than 20% (p = 0.20) live off campus, 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 n≥30\mathrm { n } \geq 30n≥30

A Small Private College Is Interested in Determining the Percentage $\mathrm { n } \geq 30$