National public opinion polls are based on interviews of as few as 1,500 people in a random sampling of public sentiment toward one or more issues. These interviews are commonly done in person, because mail returns are poor and telephone interviews tend to reach older people, thus biasing the results. Suppose that a random sample of 1,500 people determines the proportion of the adult public in agreement with recent energy conservation proposals.
a. If 560 indicate they favor the policies set forth by the current administration, estimate π, the proportion of adultsholding a “favor” opinion. Use a 95% confidence interval. What is the half width of the confidence interval?
b. How many people must the survey include to have a 95% confidence interval with a half width of .01?
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