Question

in a study of government financial aid for college students it becomes necessary to estimate the percentage of full-time college students to earn a bachelors degree in four years or less. find the sample size needed to estimate that percentage. use a 0.04 margin of error and use a confidence level of 99%.

Answer 1

Given that, margin of error (E) = 0.04

Assume that nothing is known about the percentage to be estimated so, we take p = 0.5

A 99% confidence level has significance level of 0.01 and critical value is,

Za/2 = 2.576

Excel Command : NORMSINV (0.995) = 2.576

We want to find the sample size (n),

n=p* (1 - p)* *(1-0)*(4/2)2 = 0.5*(1 -0.5) * 2.576 )' = 1036.84 0.04

=> n 1037

Therefore, required sample size is 1037

Note: if we used critical value = 2.575 then n = 1036