Question

A university dean is interested in determining the proportion of students who receive some sort of
financial aid. Rather than examine the records for all students, the dean randomly selects 200
students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the
proportion of all students receiving financial aid to within 5% with 99% confidence level, how
many students would need to be sampled?

Answer 1

Solution :

Given that n = 200 , x = 118 , margin of error E = 0.05

=> p = x/n

= 118/200

= 0.59

=> q = 1 - p = 0.41

=> For 99% confidence interval , Z = 2.58

=> Sample size n = p*q*(Z/E)^2

= 0.59*0.41*(2.58/0.05)^2

= 644.0733

= 644 (rounde to the nearest integer)

Answer 2

the answer is C