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 60% 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. A-Z DATA file Private Colleges 52.8 43.2 45.0 33.3 44.0 2. 30.6 45.8 37.8 50.5 42.0 13. Public Colleges 20.3 22.0 28.2 15.6 24.1 28.5 14. 22.8 25.8 18.5 25.6 14.4 21.8 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places. 31 = S1 = S2 = b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place. A+ Interpret this value in terms of the annual cost of attending private and public colleges. K c. Develop a 95% confidence interval of the difference between the annual cost of attending private and public colleges 95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges