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 3% with 99% reliability, how many students would need to be sampled?

Please show al work on how you got the answer.

Answer 1

Solution :

Given that,

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

= 0.59

1 - = 1-0.59 = 0.41

margin of error = E = 0.03

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z_{0.005 = 2.576}

Z/2 = 2.576

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

= (2.576/0.03)² *0.59*0.41

= 1784

sample size = n = 1784

Answer =1784 student .