You may need to use the appropriate appendix table or technology to answer this question. The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.cam). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Private Colleges Public Colleges 53.8 44.2 45.0 33.3 43.0 20.3 22.0 28.2 15.6 24.1 28.5 31.6 44.8 38.8 49.5 42.0 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 $ 42.6 q thousand sample standard deviation $ 6.74 q 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 $ "272.3 7 , , q thousand sample standard deviation $ 4.53 thousand (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private Public.) $ 20.3 q 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 $ 20.2 X more than the mean annual cost to attend public college (c) Develop a 95% condence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private Public. Round your answers to one decimal place.) $ thousand to $ thousand