The article “Should Pregnant Women Move? Linking Risks for Birth Defects with Proximity to Toxic Waste Sites” (Chance [1992]: 40– 45) reported that in a large study carried out in the state of New York, approximately 30% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that p = 0.3.
a. Would ˆ p based on a random sample of only 10 residents have a sampling distribution that is approximately nor-mal? Explain why or why not.
b. What are the mean and standard deviation of the sampling distribution of ˆ p if the sample size is 400?
c. Suppose that the sample size is n = 200 rather than n = 400. Does the change in sample size affect the mean and standard deviation of the sampling distribution of ˆ p ? If so, what are the new values for the mean and standard deviation? If not, explain why not.