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
53.8
44.2
45.0
32.3
44.0
29.6
46.8
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 (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)
Sample mean: $ 41.40 thousand
Sample standard deviation: $ 7.68 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: $ 22.08 thousand
Sample standard deviation: $ 4.99 thousand
(b)
What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.)
Point estimate: $ 19.32 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 $ 19,320 more than the mean annual cost to attend public college.