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 a0.04 margin of error and use a confidence level of 90​%.

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

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

nequals=nothing

​(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.)

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

A.

​No, using the additional survey information from part​ (b) does not change the sample size.

B.

​No, using the additional survey information from part​ (b) only slightly reduces the sample size.

C.

​Yes, using the additional survey information from part​ (b) only slightly increases the sample size.

D.

​Yes, using the additional survey information from part​ (b) dramatically reduces the sample size.

Answer 1

Margin of error ( E ) = 0.04

confidence level = 90%

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

a) assume that nothing is known about the percentage to be estimated then, p= 0.5

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

n = 423

b) if, proportion of p = 0.40 then sample size of n is,

n = 406

c) since, 406 is slightly less than 423 there is not much effect on sample size of additional information.

=> no, using the additional survey information from part b) only slightly reduces the sample size.