Question

In: Statistics and Probability

​ In a study of government financial aid for college​ students, it becomes necessary to estimate...

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

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

___ ​(Round up to the nearest​ integer.)

b. Assume prior studies have shown that about 60​% 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) 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) only slightly increases the sample size.

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

Solutions

Expert Solution

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.05

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 /0.05 )2 * 0.5 * 0.5

= 384.16

sample size = n = 385

b) = 0.60

1 - = 1 - 0.60 = 0.40

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 /0.05 )2 * 0.60 * 0.40

= 368.79

sample size = n = 369

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


Related Solutions

In a study of government financial aid for college​ students, it becomes necessary to estimate the...
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....
In a study of government financial aid for college students, it becomes necessary to estimate the...
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 bachelors 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 99%. A. Assume that nothing is known about the percentage to be estimated N = B. Assume prior studies have shown that about 35% of full time...
In a study of government financial aid for college​ students, it becomes necessary to estimate the...
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 95​%. Complete parts​ (a) through​ (c) below. a. Assume that nothing is known about the percentage to be estimated. ​(Round up to the nearest​ integer.) N=600 b. Assume...
In a study of government financial aid for college​ students, it becomes necessary to estimate the...
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 99​%. 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....
In a study of government financial aid for college​ students, it becomes necessary to estimate the...
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 99%. Complete parts​ (a) through​ (c) below. 1) Assume that nothing is known about the percentage to be estimated. n= 2)Assume prior studies have shown that about 45%of​...
In a study of government financial aid for college​ students, it becomes necessary to estimate the...
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​ (c) below. a. Assume that nothing is known about the percentage to be estimated. n=________(Round up to the nearest​ integer.) b. Assume prior...
In a study of government financial aid for college​ students, it becomes necessary to estimate the...
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 = ? ​(Round up to the nearest​ integer.)...
n a study of government financial aid for college​ students, itbecomes necessary to estimate the...
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 95​%. 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....
In a study of government financial aid for college students, they need to estimate the percentage...
In a study of government financial aid for college students, they need to estimate the percentage of students who graduate in four years. Find the sample size needed to estimate the percentage. Use a 4% margin of error, and 90% confidence level. 1. A previous study showed that 60% graduate in four years. 2. We don't know the percentages at all
A study was being done to estimate the proportion of students who receive financial aid. If...
A study was being done to estimate the proportion of students who receive financial aid. If the study would like to construct 95% confidence interval for the proportion of students receiving financial aid within 3%, what sample size would be needed? A previous study stated that 57% of students receive some form of financial aid.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT