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​%.

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

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

n= _____

​(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.

n= _____

​(Round up to the nearest​ integer.)

Answer 1

The minimum sample size for proportion with given margin of error is at 90% confidence level is calculated as:

Where is the prior assumptions, E is the margin of error which is 0.04 and the Zc at 90% confidence level is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.95), thus computed as Zc = 1.645

a) Assuming that nothing is known about the percentage hence the is assumed as 0.50.

Thus the minimum sample is calculated as:

b. Assume prior studies have shown that about 40​% of​ full-time students earn​ bachelor's degrees in four years or less, hence the be 0.40.

Now the minimum sample is calculated as:

Note: Feel free to ask if problem remains