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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.


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 0.05 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= (Round 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) 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) dramatically reduces the sample size. 

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

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Answer #1

a)

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.05

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.1 is 1.64.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.64/0.05)^2
n = 268.96

Therefore, the sample size needed to satisfy the condition n >= 268.96 and it must be an integer number, we conclude that the minimum required sample size is n = 269
Ans : Sample size, n = 269


b)

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.05

The provided estimate of proportion p is, p = 0.45
The critical value for significance level, α = 0.1 is 1.64.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.45*(1 - 0.45)*(1.64/0.05)^2
n = 266.2704

Therefore, the sample size needed to satisfy the condition n >= 266.2704 and it must be an integer number, we conclude that the minimum required sample size is n = 266
Ans : Sample size, n = 266

c)

Option B)

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