Assume that the population is normally distributed. The out-of-state tuitions (in dollars) for random samples of both public and private four-year colleges in a New England state are collected and listed below. Public School Private School Sample size 7 6 Sample mean $9,039.9 $16,147.5 Sample standard deviation $3,325.5 $4,023.7 Find the 99% confidence interval of the difference in the means. Solution Given a=0.01, t(0.005, df=n1+n2-2=7+6-2=11)=3.11 (check student t table) So 99% CI is (xbar1 - xbar2) ± t*[s1^2/n1 + s2^2/n2] --> (9039.9-16147.5) ± 3.11*sqrt(3325.5^2/7+ 4023.7^2/6) --> (-13540.27, -674.9273).