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 99% confident that your estimate is within 0.02 of the true proportion? A sample size of is needed. (Doudun to the noroet whole number

Answer 1

Solution :

Given that,

$\hat p$ = 0.25

1 - $\hat p$ = 1 - 0.25 = 0.75

margin of error = E = =0.02

At 99% confidence level the z is,

$\alpha$ = 1 - 99%

$\alpha$ = 1 - 0.99 = 0.01

$\alpha$/2 = 0.005

Z_$\alpha$/2 = 2.58 ( Using z table ( see the 0.005 value in standard normal  (z) table corresponding z value is 2.58 )

Sample size = n = (Z_$\alpha$/2 / E)² * $\hat p$ * (1 - $\hat p$ )

= (2.58 / 0.02)² * 0.25 * 0.75

=3120

Sample size = 3120