A college believes that 28% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the
A) 287
B) 861
C) 1292
D) 1464

Question

Quizplus · Accepted Answer

The sample size necessary for estimating a proportion with a specified margin of error can be calculated using the formula:
n=((z*sqrt(p*(1-p)))/E)^2
where z is the z-score associated with the level of confidence desired, p is the estimated proportion, and E is the desired margin of error.
Assuming a 95% level of confidence (z=1.96) and a margin of error of 3%, the necessary sample size is:
n=((1.96*sqrt(0.28*(1-0.28)))/0.03)^2 = 860.53
Since sample size must be a whole number, we round up to the nearest integer, giving a sample size of 861.

A College Believes That 28% of Applicants to That School