Question

When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their maling 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 p 0.05 and constructed the histogram of the 1000 sample proportions, as shown in the accompanying 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. Samples of size 20 Samples of size 50 0.00 0.25 0.00 0.15 Sample Proportions Sample Proportions Samples of scze 100 G Samples of size 200 150 100 100- 50 0.15 0.15 Sample Proportions As the sample size increases, the center of the histogram the shape of the distribution . and the variability/spread in the sample proportion increases decreases stays approximately the same becomes more Normal becomes less Normal QUESTION 2

Answer 1

As the sample size increases the centre of histogram tends to 0.05, the shape of the distribution becomes bell-shaped, and variability in the sample proportion becomes more normal.

Sufficiently large sample from a population with a finite level of variance, the mean of all samples will tend towards population mean.