The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Click on the datafile logo to reference the data. Round degrees of freedom to the preceding whole number. Private colleges.
52.8 43.2 45.0 33.3 44.0
30.6 45.8 37.8 50.5 42.0
Public colleges.
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8a. Compute the sample mean and sample standard deviation for private and public colleges. b. What is the point estimate of the difference between the two population means? c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.