The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed.† The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Private Colleges 52.8 42.2 44.0 33.3 45.0 29.6 44.8 36.8 51.5 43.0 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 = ? thousand sample 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 = ? thousand sample 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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed.† The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.

Private Colleges

52.8	42.2	44.0	33.3	45.0
29.6	44.8	36.8	51.5	43.0

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 = ? thousand

sample 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 = ? thousand

sample 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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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