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 0.02 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. n=______d up to the nearest integer.)

b. Assume prior studies have shown that about 45% of full-time students earn bachelor's degrees in four years or less. n=_______ (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) only slightly reduces the sample size.

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

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

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

Answer #1

Part a

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are not given the estimate for proportion, so we take

p = 0.5

q = 1 – p = 0.5

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Margin of error = E = 0.02

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.5*0.5*(1.6449/0.02)^2

n = 1691.06

Required sample size = 1692

Part b

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are not given the estimate for proportion, so we take

p = 0.45

q = 1 – p = 0.55

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Margin of error = E = 0.02

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.45*0.55*(1.6449/0.02)^2

n = 1674.149

Required sample size = 1675

Part c

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

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