Question

A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points with 99% confidence?

Answer 1

Use the following expression for the number of elements of a sample, related to a certain proportion a Z-score:

`n=((Z)/(E))^2\cdot p\cdot q`

where,

p: percentage of applicants in decimal form = 0.22 (28%)

q = 1 - p = 1 - 0.22 = 0.78

E: percentage margin = 0.05 (5%)

Z-score for 99% confidence = 2.576 (found in a Z-score table)

Replace the previous values of the parameters into the formula for n and simplify:

`n=((2.576)/(0.06))^2\cdot0.22\cdot0.78\approx316`

Hence, approximately 316 students are needed for the sample.