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wrote...
Posts: 215
2 weeks ago
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.

The admissions officers want to estimate the true percentage of private school applicants to within ±4%, with 90% confidence. How many applications should they sample?
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
Read 46 times
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Answer verified by a subject expert
wrote...
Posts: 238
2 weeks ago
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ME = z*
0.04 = 1.645
=
n = 178.60 ≈ 179
They should sample at least 179 applicants. (423 if = 0.5 is used)
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wrote...
2 weeks ago
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.

They actually select a random sample of 450 applications, and find that 46 of those students attend private schools. Create the confidence interval.
wrote...
2 weeks ago
We have a random sample of less than 10% of the applicants, with 46 successes and 404 failures, both of which are at least ten, so a Normal model applies.  The confidence interval is (0.079, 0.126).
wrote...
2 weeks ago
Appreciate the effort, thank you!
wrote...
2 weeks ago
You're very welcome ... please mark the topic solved when you get a chance
wrote...
2 weeks ago
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.

Interpret the confidence interval in this context.
wrote...
2 weeks ago
We are 90% confident that between 7.9% and 12.6% of the applicants attend private high schools.
wrote...
2 weeks ago
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.

Should the admissions officers conclude that the percentage of private school students in their applicant pool is lower than the statewide enrollment rate of 12%? Explain.
wrote...
2 weeks ago
No. Since 12% lies in the confidence interval it's possible that the percentage of private school students in the applicant pool matches the statewide enrollment rate.
wrote...
2 weeks ago
I appreciate what you did here, answered it correctly Smiling Face with Open Mouth
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