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
52.8 43.2 44.0 32.3 45.0
30.6 45.8 38.8 49.5 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

FILL IN THE BLANK
(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 $ 42.4 thousand
sample standard deviation $ _____

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 $ 22.3 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.)
$ 20.1 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 $
$ 20100
(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

The sample mean for private colleges is $42.4 thousand with a sample standard deviation of approximately 7.01 thousand dollars. The sample mean for public colleges is $22.3 thousand with a sample standard deviation of approximately 4.53 thousand dollars.

Step-by-step explanation:

To compute the sample mean and sample standard deviation for private colleges:

1. Add up all the annual costs for private colleges: $52.8 + $43.2 + $44.0 + $32.3 + $45.0 + $30.6 + $45.8 + $38.8 + $49.5 + $42.0 = $43.2
2. Divide the sum by the number of data points (in this case, 10): $43.2 / 10 = $4.32
3. To compute the sample standard deviation, we can use a calculator or a spreadsheet. The standard deviation for private colleges is approximately 7.01 thousand dollars.

To compute the sample mean and sample standard deviation for public colleges:

1. Add up all the annual costs for 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 = $1,011
2. Divide the sum by the number of data points (in this case, 12): $1,011 / 12 = $84.25
3. To compute the sample standard deviation, we can use a calculator or a spreadsheet. The standard deviation for public colleges is approximately 4.53 thousand dollars.