You may need to use the appropriate appendix table or technology to answer this question. 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. 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. Private Colleges Public Colleges 51.8 44.2 45.0 33.3 44.0 20.3 22.0 28.2 15.6 24.1 28.5 29.6 46.8 36.850.5 41.0 22.8 25.8 18.5 25.6 14.4 21.8 (a) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.) sample mean $ thousand sample standard deviation $ thousand Compute the sample mean (in thousand dollars) and sample standard deviation in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.) sample mean $ thousand sample standard deviation thousand $ (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private - Public.) $ thousand Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges. We estimate that the mean annual cost to attend private colleges is $ more than the mean annual cost to attend public college