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 0.03 margin of error and use a confidence level of 99​%.

Complete parts​ (a) through​ (c) below.

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

N=1844

​(Round up to the nearest​ integer.)

b. Assume prior studies have shown that about 40​% of​ full-time students earn​ bachelor's degrees in four years or less. ​(Round up to the nearest​ integer.)

Answer 1

Given : Margin of error=E=0.03

Signifiacnce level=

From standard normal distribution table ,

a) Since , there is nothing to know the estimate of percentage

Therefore , assume that p=q=0.5

Therefore , the required sample size is ,

b) Since , p=0.40 , q=1-p=0.60

Therefore , the required sample size is ,