Question

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.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.

Private Colleges

53.8	42.2	46.0	32.3	45.0
30.6	44.8	37.8	51.5	41.0

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$  thousandsample 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$  thousandsample 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

(c)

Develop a 95% confidence 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

Answer 1

a)

For private colleges,

sample mean = 42.5

sample standard deviation = 7.47

For public colleges,

sample mean = 22.3

sample standard deviation = 4.53

b) Let denote the mean annual cost of attending private and public colleges respectively.

The point estimate (in thousand dollars) of the difference between the two population means is

=

c)

Lower limit = 14.4

Upper limit = 26