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a) Looking at the histograms, what is the smallest sample size you would be comfortable using the Normal model as an approximation for the sampling distribution?

a) Looking at the histograms, what is the smallest sample size you would be comfortable using the Normal model as an approximation for the sampling distribution?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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= An automatic character recognition device successfully reads about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75, and 100. For each sample size, they simulated 1000 samples with success rate p = 0.85 and constructed the histogram of the 1000 sample proportions. The histograms, sample statistics, and theoretical values are shown in the accompanying tables. Complete parts a and b below. Click the icon to view the sample statistics and theoretical values. Click the icon to view the histograms. a) Looking at the histograms, what is the smallest sample size you would be comfortable using the Normal model as an approximation for the sampling distribution? A. The Normal model would be reasonable to use for a sample size of at least 100. B. The Normal model would be reasonable to use for a sample size of at least 50. OC. The Normal model would be reasonable to use for a sample size of at least 20. D. The Normal model would be reasonable to use for a sample size of at least 75. b) What does the Success/Failure Condition say about what sample size should be used? A. The Success/Failure Condition is satisfied for sample sizes of at least 20. B. The Success/Failure Condition is satisfied for sample sizes of at least 75. OC. The Success/Failure Condition is satisfied for sample sizes of at least 100. O D. The Success/Failure Condition is satisfied for sample sizes of at least 50.
Transcribed Image Text:= An automatic character recognition device successfully reads about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75, and 100. For each sample size, they simulated 1000 samples with success rate p = 0.85 and constructed the histogram of the 1000 sample proportions. The histograms, sample statistics, and theoretical values are shown in the accompanying tables. Complete parts a and b below. Click the icon to view the sample statistics and theoretical values. Click the icon to view the histograms. a) Looking at the histograms, what is the smallest sample size you would be comfortable using the Normal model as an approximation for the sampling distribution? A. The Normal model would be reasonable to use for a sample size of at least 100. B. The Normal model would be reasonable to use for a sample size of at least 50. OC. The Normal model would be reasonable to use for a sample size of at least 20. D. The Normal model would be reasonable to use for a sample size of at least 75. b) What does the Success/Failure Condition say about what sample size should be used? A. The Success/Failure Condition is satisfied for sample sizes of at least 20. B. The Success/Failure Condition is satisfied for sample sizes of at least 75. OC. The Success/Failure Condition is satisfied for sample sizes of at least 100. O D. The Success/Failure Condition is satisfied for sample sizes of at least 50.
mpted Sample Statistics and Theoretical Values estion 6 estion 7 estion 8 estion 9 estion 1 estion 11 estion 11 n 20 50 75 100 # of Samples Observed Mean 0.8465 0.8405 0.8402 0.8487 Histograms # of Samples Samples of size 20 400- 300- 200- 100- 0- 0.5 Print 100- 50- Samples of size 75 250 200- 150- 0+ 0.65 Theoretical Mean Sample Proportions 1.0 1.0 Sample Proportions 0.85 0.85 0.85 0.85 Q O Done The Nomar mouer would be Teasonable to use for a Observed st.dev. 0.1005 0.0616 0.0541 0.0654 # of Samples # of Samples Samples of size 50 400- 300- 200- 100- 0- 0.65 Theoretical st.dev. 0.0798 0.0505 0.0412 0.0357 200- 150- 100- 50- Samples of size 100 250- Sample Proportions 0- 0.7 1.0 0.9 Sample Proportions - X ra ra ra hat hple hple hple hple
Transcribed Image Text:mpted Sample Statistics and Theoretical Values estion 6 estion 7 estion 8 estion 9 estion 1 estion 11 estion 11 n 20 50 75 100 # of Samples Observed Mean 0.8465 0.8405 0.8402 0.8487 Histograms # of Samples Samples of size 20 400- 300- 200- 100- 0- 0.5 Print 100- 50- Samples of size 75 250 200- 150- 0+ 0.65 Theoretical Mean Sample Proportions 1.0 1.0 Sample Proportions 0.85 0.85 0.85 0.85 Q O Done The Nomar mouer would be Teasonable to use for a Observed st.dev. 0.1005 0.0616 0.0541 0.0654 # of Samples # of Samples Samples of size 50 400- 300- 200- 100- 0- 0.65 Theoretical st.dev. 0.0798 0.0505 0.0412 0.0357 200- 150- 100- 50- Samples of size 100 250- Sample Proportions 0- 0.7 1.0 0.9 Sample Proportions - X ra ra ra hat hple hple hple hple
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