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 paren…

Question

asked Aug 6, 2023 134k views

1 Answer

Faly · Answer 1 · 2023-08-10T08:57:38+0000

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.