According to a recent report by the PEW Research Center, 85% of adults under 30 feel optimistic about the economy, but the optimism is shared by only 45% of those who are over 50 (Newsweek , September 13, 2010). A research analyst would like to construct 95% confidence intervals for the proportion patterns in various regions of the country. She uses the reported rates by the PEW Research Center to determine the sample size that would restrict the margin of error to within 0.05.
a. How large a sample is required to estimate the proportion of adults under 30 who feel optimistic about the economy?
b. How large a sample is required to estimate the proportion of adults over 50 who feel optimistic about the economy?