When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50, 100, and 200. For each sample size they simulated 1000 mailings with success rate p=0.05 and constructed the histogram of the 1000 sample proportions, shown in the accompanying link. Explain what these histograms say about the sampling distribution model for sample proportions. Be sure to talk about shape, center. and spread. Click the icon to view histograms of the simulations. Discuss how the shape changes with sample size. OA. The distributions for small samples are left-skewed but are more symmetric as n increases. OB. The distributions for small samples are right-skewed and get more left-skewed as n increases. OC. The distributions for small samples are right-skewed but are more symmetric as n increases. OD. The distributions for small samples are left-skewed and get more right-skewed as n increases. O E. The shape does not change with sample size. Histograms of the Simulations Samples of Size 20 400- Samples of Size 5 300- X

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When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50, 100, and 200. For each sample size
they simulated 1000 mailings with success rate p = 0.05 and constructed the histogram of the 1000 sample proportions, shown in the accompanying link. Explain what these histograms say about the sampling distribution model for sample proportions. Be sure to talk about shape, center.
and spread.
Click the icon to view histograms of the simulations.
Discuss how the shape changes with sample size.
OA.
A. The distributions for small samples are left-skewed but are more symmetric as n increases.
OB. The distributions for small samples are right-skewed and get more left-skewed as n increases.
OC. The distributions for small samples are right-skewed but are more symmetric as n increases.
O D.
D. The distributions for small samples are left-skewed and get more right-skewed as n increases.
O E.
E. The shape does not change with sample size.
Histograms of the Simulations
Number of San
Samples of Size 20
400-
Samples of Size
100
200
0.25
Sample Proportions
0.14
Sample Proportions
Q
Q
L
Number
Number of Samples
Samples of Size 5
300-
Samples of Size
200
150-
Sample Proporti
0-
Sample Proporti
- X
Transcribed Image Text:When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50, 100, and 200. For each sample size they simulated 1000 mailings with success rate p = 0.05 and constructed the histogram of the 1000 sample proportions, shown in the accompanying link. Explain what these histograms say about the sampling distribution model for sample proportions. Be sure to talk about shape, center. and spread. Click the icon to view histograms of the simulations. Discuss how the shape changes with sample size. OA. A. The distributions for small samples are left-skewed but are more symmetric as n increases. OB. The distributions for small samples are right-skewed and get more left-skewed as n increases. OC. The distributions for small samples are right-skewed but are more symmetric as n increases. O D. D. The distributions for small samples are left-skewed and get more right-skewed as n increases. O E. E. The shape does not change with sample size. Histograms of the Simulations Number of San Samples of Size 20 400- Samples of Size 100 200 0.25 Sample Proportions 0.14 Sample Proportions Q Q L Number Number of Samples Samples of Size 5 300- Samples of Size 200 150- Sample Proporti 0- Sample Proporti - X
Discuss how the shape changes with sample size.
OA. The distributions for small samples are left-skewed and get more right-skewed as n increases.
OB. The distributions for small samples are left-skewed but are more symmetric as n increases.
OC. The distributions for small samples are right-skewed and get more left-skewed as n increases.
OD. The distributions for small samples are right-skewed but are more symmetric as n increases.
OE. The shape does not change with sample size.
Discuss how the center changes with sample size.
OA. The center approaches the population proportion of 0.05 as n increases.
OB. The center approaches the population proportion of 0.05 as n decreases.
OC. The center varies seemingly independent of sample size.
OD. The center does not change with sample size; all the histograms are centered near 0.05.
Discuss how the variability changes with sample size.
OA. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions decreases.
OB. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions increases
OC. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions increases.
OD. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions decreases
Transcribed Image Text:Discuss how the shape changes with sample size. OA. The distributions for small samples are left-skewed and get more right-skewed as n increases. OB. The distributions for small samples are left-skewed but are more symmetric as n increases. OC. The distributions for small samples are right-skewed and get more left-skewed as n increases. OD. The distributions for small samples are right-skewed but are more symmetric as n increases. OE. The shape does not change with sample size. Discuss how the center changes with sample size. OA. The center approaches the population proportion of 0.05 as n increases. OB. The center approaches the population proportion of 0.05 as n decreases. OC. The center varies seemingly independent of sample size. OD. The center does not change with sample size; all the histograms are centered near 0.05. Discuss how the variability changes with sample size. OA. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions decreases. OB. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions increases OC. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions increases. OD. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions decreases
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