5.11 Sampling distributions and sample size. The software JMP includes some applets, one of which is called “Sampling Distribution of Sample Proportions.” This applet does sampling very quickly, especially if “Animate Illustration?” is set to No.

a. In Exercise 5.7, you obtained 50 draws of size n=25 when p=0.4 .

Use this JMP applet to generate 500 draws of size n=25 when p=0.4 .

What is the mean of the sample proportions, and what is the standard deviation?

b. Keeping p=0.4 , generate 500 draws for sample sizes n=100

, 400, and 1600. For each sample size record the mean and standard deviation of the sample proportions. Also explain why p^

appears to be an unbiased estimator.

c. Each sample size is four times larger than the previous one. For each adjacent pair compute the ratio of means and the ratio of standard deviations using the larger sample size in the denominator. Comment on what you find.