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Hie average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearhcr a third of the annual income of a typical familyr with collegeage children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the tvpical 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 datale logo to reference the data. 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 21.8 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places. x_1= 51 = I F2= s2 = .- b. what is the point estimate of the difference between the two population means? Round vour answer to one decimal place. Interpret this value in terms of the annual cost of attending private and public colleges. $2 c. Develop a 95% condence interval of the difference between the annual cost of attending private and pubic colleges. Round your answer to hundreds. Use ttable. From 95% condence interval, private colleges have a population mean annual cost $5 = to 3; = which is more expensive than public colleges. Check My Work