When they send out their fundraising letter, a philanthropic organization typically gets a return from about...

 

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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. W Click the icon to view histograms of the simulations. Discuss how the shape changes with sample size. O A. The distributions for small samples are left-skewed and get more right-skewed as n increases. O B. The distributions for small samples are left-skewed but are more symmetric as n increases. O C. The distributions for small samples are right-skewed and get more left-skewed as n increases. O D. The distributions for small samples are right-skewed but are more symmetric as n increases. O E. The shape does not change with sample size. Discuss how the center changes with sample size. O A. The center approaches the population proportion of 0.05 as n increases. O B. The center approaches the population proportion of 0.05 as n decreases. O C. The center varies seemingly independent of sample size. O D. The center does not change with sample size; all the histograms are centered near 0.05. Discuss how the variability changes with sample size. O A. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions decreases. O B. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions increases. O C. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions decreases. O D. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions increases. 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. W Click the icon to view histograms of the simulations. Discuss how the shape changes with sample size. O A. The distributions for small samples are left-skewed and get more right-skewed as n increases. O B. The distributions for small samples are left-skewed but are more symmetric as n increases. O C. The distributions for small samples are right-skewed and get more left-skewed as n increases. O D. The distributions for small samples are right-skewed but are more symmetric as n increases. O E. The shape does not change with sample size. Discuss how the center changes with sample size. O A. The center approaches the population proportion of 0.05 as n increases. O B. The center approaches the population proportion of 0.05 as n decreases. O C. The center varies seemingly independent of sample size. O D. The center does not change with sample size; all the histograms are centered near 0.05. Discuss how the variability changes with sample size. O A. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions decreases. O B. As n gets smaller, the histograms approach the Normal shape, and the variability in the sample proportions increases. O C. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions decreases. O D. As n gets larger, the histograms approach the Normal shape, and the variability in the sample proportions increases.

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According to the Central Limit Theorem for Sample Proportions the theoretical means and standard dev... View the full answer