Suppose a realtor is interested in comparing the asking prices of midrange homes in Peoria, Illinois, and Evansville, Indiana. The realtor conducts a small telephone survey in the two cities, asking the prices of midrange homes. A random sample of 21 listings in Peoria resulted in a sample average price of $116,900, with a standard deviation of $2,300. A random sample of 26 listings in Evansville resulted in a sample average price of $114,000, with a standard deviation of $1,750. The realtor assumes prices of midrange homes are normally distributed and the variance in prices in the two cities is about the same.

a. What would he obtain for a 90% confidence interval for the difference in mean prices of midrange homes between Peoria and Evansville?

b. Test whether there is any difference in the mean prices of midrange homes of the two cities for α = .10.