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​% ​reliability, how many students would need to be​ sampled?

a.) 156

b.) 642

c.) 250

d.) 33

Answer 1

Solution :

Given that,

n = 200

x = 118

Point estimate = sample proportion = = x / n = 118 / 200 = 0.59

?̂ = 1 - = 1 - 0.59 = 0.41

margin of error = E = 0.05

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.575

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.575 / 0.05)2 * 0.59 * 0.41

= 641.57

sample size = n = 642

correct option is = b