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 Public Colleges 52.8 44.2 46.0 32.3 20.3 31.6 45.0 44.8 36.8 51.5 43.0 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 $ 42.8 thousand sample standard deviation $ 7.21 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 $ 22.3 thousand thousand sample standard deviation $ 4.53 (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private Public.) $ 20.5 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 $ 21 x 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.) $15.4 X thousand to $ 25.6 X thousand

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18th Edition
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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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
Public Colleges
52.8 44.2 46.0 32.3
20.3
31.6
45.0
44.8 36.8 51.5 43.0
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
$ 42.8
thousand
sample standard deviation
$ 7.21
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
$ 22.3
thousand
thousand
sample standard deviation
$ 4.53
(b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private Public.)
$ 20.5
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 $ 21
x 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.)
$15.4
X thousand to $ 25.6
X thousand
Transcribed Image Text: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 Public Colleges 52.8 44.2 46.0 32.3 20.3 31.6 45.0 44.8 36.8 51.5 43.0 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 $ 42.8 thousand sample standard deviation $ 7.21 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 $ 22.3 thousand thousand sample standard deviation $ 4.53 (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private Public.) $ 20.5 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 $ 21 x 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.) $15.4 X thousand to $ 25.6 X thousand
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