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​ bachelor's 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 90​%.

a.) Assume that nothing is known about the percentage to be estimated.

b.) Assume prior studies have shown that about 40% of full time students earn BA degrees in 4 years or less

c.) Does the added knowledge in part b have much of an effect on the sample size?

Answer 1

Solution :

Given that,

Z_/2 = 1.645

(a)

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

= (1.645 / 0.04)² * 0.5 * 0.5

= 423

sample size = n = 423

(b)

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

= (1.645 / 0.04)² * 0.40 * 0.60

= 406

sample size = n = 406

(c)

Having an estimate of the population proportion reduces the minimum sample size is needed .