Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research on other college​ campuses, you believe the proportion will be near 25​%.

What sample size is needed if you wish to be 90​% confident that your estimate is within 0.02 of the true​ proportion?

Answer 1

Solution:

Given that,

= 0.25

1 - = 1 - 0.25 = 0.75

margin of error = E = 0.02

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= (1.645 / 0.02)2 * 0.25 * 0.75

=1268

n = sample size = 1268