Question

in a study of government financial aid for college students, it becomes necessary to estimate the percentage of full time college students who earn a bachelors degree in four years or leas. find the sample size needed to estimate the percentage. use a 0.02 margin of error and use a confidence level of 90%

A. assume that nothing is known about the percentage to be estimated

B. assume prior studies have shown that about 35% of full time students earn bachelors degrees in four years or less

C. does the added knowledge in part B have much effect on the sample size?

Answer 1

Given that, margin of error (E) = 0.02

A 90% confidence level has significance level of 0.10 and critical value is,

A) If we don't know about the percentage to be estimated, so we assume, it to be 50%. That is, p = 0.5

We want to find, the sample size (n),

Therefore, required sample size is 1691.

b) Given that, p = 0.35, then sample size (n) is,

Therefore, required sample size is 1539.

c) Added knowledge in part B) reduces the required sample size.

Note: if you want sample size is nearest to next whole number, then sample size in part a) and part b) are, n = 1692 and n = 1540 respectively.