In a recent survey of home-buyer preferences, consumers were asked about desired characteristics, such as a wood-burning fireplace, a den/ library, and flooring. In particular, each person was asked...

In a recent survey of home-buyer preferences, consumers were asked about desired characteristics, such as a wood-burning fireplace, a den/ library, and flooring. In particular, each person was asked whether a separate dining room is essential. The sample size and the number who responded “Yes” to this question are given in the table below by geographic region.

a. Find a 99% confidence interval for the true proportion of home-buyers who believe a separate dining room is essential in each geographic region.

 b. Which confidence interval in part (a) is the largest? Why?