When they send out their fundraising letter?, a philanthropic organization typic

Question

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 in the? future, they did a simulation using samples of size? 20, 50,? 100, and 200. For each sample? size, they simulated 1000 mailings with success rate pequals0.05 and constructed the histogram of the 1000 sample? proportions, as shown in the accopmanying table. Explain how these histograms demonstrate what the Central Limit Theorem says about the sampling distribution model for sample proportions. Be sure to talk about? center, shape, and spread

As the sample size? increases, the center of the histogram (moves to the left/moves to the right/stays approximately the same), the shape of the distribution (becomes less normal/stays approximately the same/becomes more normal), and the variability in the sample proportions (decreases/increases/stays approximately the same). These simulations (do not appear/appear) to demonstrate what the Central Limit Theorem says about the sampling distribution model for sample proportions.

Samples of size 20 400 Samples of size 50 300 ? ? ? ? 200- 200 E3 E3 0.00 0.25 0.00 0.15 Sample Proportions Sample Proportions Samples of size 100Samples of size 200 a 200 150 ? ? ? ? 100 50 E3 E3 0.00 0.15 0.00 0.15 Sample Proportions Sample Proportions

Explanation / Answer

(a)

As the sample size increases, the center of the histogram moves to the right., the shape of the distribution becomes more normal, the variability in the sample proportions decreases. These simulations appear to demonstrate what the central Limit Theorem says about the sampling distribution model for sample proportions.

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