When members of a philanthropic organization send out a fundraising letter, they get a return from about 7% of the people on their mailing list. They simulated 1000 mailings for samples of size n with success rate p=0.07. The sample statistics from each simulation are shown in the table. Complete partsa) through c). n mean standard dev. 20 0.0692 0.0565 50 0.0692 0.0368 100 0.0703 0.0251 200 0.0705 0.0181 a) According to the central limit theorem, what should the theoretical mean and standard deviation be for each of the sample sizes? Complete the following table. n theoretical mean theoretical standard dev. 20 nothing nothing 50 nothing nothing 100 nothing nothing 200 nothing nothing (Round to four decimal places as needed.) b) How close are the theoretical values to those that were observed? Not close Very close c) At what sample size are you comfortable using the normal approximation based on the success/failure condition? A. 200 B. 20 C. 100 D. 50
When members of a philanthropic organization send out a fundraising letter, they get a return from about 7% of the people on their mailing list. They simulated 1000 mailings for samples of size n with success rate p=0.07. The sample statistics from each simulation are shown in the table. Complete partsa) through c). n mean standard dev. 20 0.0692 0.0565 50 0.0692 0.0368 100 0.0703 0.0251 200 0.0705 0.0181 a) According to the central limit theorem, what should the theoretical mean and standard deviation be for each of the sample sizes? Complete the following table. n theoretical mean theoretical standard dev. 20 nothing nothing 50 nothing nothing 100 nothing nothing 200 nothing nothing (Round to four decimal places as needed.) b) How close are the theoretical values to those that were observed? Not close Very close c) At what sample size are you comfortable using the normal approximation based on the success/failure condition? A. 200 B. 20 C. 100 D. 50
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Question
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When members of a philanthropic organization send out a fundraising letter, they get a return from about
7%
of the people on their mailing list. They simulated 1000 mailings for samples of size n with success rate
p=0.07.
The sample statistics from each simulation are shown in the table. Complete partsa) through c). |
|
a) According to the central limit theorem, what should the theoretical mean and standard deviation be for each of the sample sizes?
Complete the following table.
|
n
|
theoretical mean
|
theoretical standard dev.
|
|
|
20
|
nothing
|
nothing
|
|
|
50
|
nothing
|
nothing
|
|
|
100
|
nothing
|
nothing
|
|
|
200
|
nothing
|
nothing
|
|
(Round to four decimal places as needed.)
b) How close are the theoretical values to those that were observed?
Not close
Very close
c) At what sample size are you comfortable using the normal approximation based on the success/failure condition?
200
20
100
50
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