National public opinion polls are often based on as few as 1,500 persons in a random sampling of public sentiment on issues of public interest. These surveys are often done in ­person because the response rate for a mailed survey is very low and telephone interviews tend to reach a larger proportion of older persons than would be represented in the public as a whole. Suppose a random sample of 1,500 registered voters was surveyed about energy ­issues.
a. If 230 of the 1,500 responded that they would favor drilling for oil in national parks, estimate the proportion π of registered voters who would favor drilling for oil in ­national parks. Use a 95% confidence interval.
b. How many persons must the survey include to have 95% confidence that the sample proportion is within .01 of π?
c. A congressman has claimed that over half of all registered voters would support drilling in national parks. Use the survey data to evaluate the congressman’s claim. Use a = .05.