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 = .3.
a. Would p^ based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not.
b. What are the mean value and standard deviation of p^ based on a random sample of size 400?
c. When n = 400, what is P(.25 ≤ p^ ≤ .35)?
d. Is the probability calculated in Part (c) larger or smaller than would be the case if n = 500? Answer without actually calculating this probability.