Question: Rex "Scooper" Hunt is running for county dog catcher. His campaign manager collected some preliminary data, and found that, among registered voters in the county, 16 out of 40 favored Rex for this elected post.

a) How large a sample of voters should the campaign manager survey in order to be 96% confident about the true population proportion of voters who favor Rex as county dog catcher?

b) Construct an 84% confidence interval that estimates the true population proportion of voters who favor Rex as county dog catcher.