Develop a 99% confidence interval of the difference between the mean annual cost of attending private and public colleges Hypothesized MeanDifferencedft StatP(T<=t) one-tailP(T<=t) two-tail015--0.0000005250.000001005 X+5. The average annual cost (including tuition, room, board, books, and fees) to attend a publiccollege takes nearly a third of the annual income of a typical family with college-age children(Money, April 2012). At private colleges, the average annual cost is equal to about 60% of theand public colleges. Data are in thousands of dollars.typical family's income. The following random samples show the annual cost of attending privatePrivate 52.8 43.2 4533.3 4430.6 45.8 37.8 50.5 42Public 20.3 2228.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8We want to conduct a hypothesis test to determine whether the cost of attending private collegesis significantly higher than the cost of attending public colleges. Use a = 0.05. A portion of EXCELoutputs is displayed in the following table.t-Test: Two-Sample Assuming UnequalVariancesPrivatePublic42.522.3Mean48.720.5Variance1210ObservationsHypothesized MeanDifferencedft Stat015COCMacBook Pro

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Develop a 99% confidence interval of the difference between the mean annual cost of attending private and public colleges

Hypothesized Mean
Difference
df
t Stat
P(T<=t) one-tail
P(T<=t) two-tail
0
15
--
0.000000525
0.000001005

X
+
5. 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
(Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the
and public colleges. Data are in thousands of dollars.
typical family's income. The following random samples show the annual cost of attending private
Private 52.8 43.2 45
33.3 44
30.6 45.8 37.8 50.5 42
Public 20.3 22
28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8
We want to conduct a hypothesis test to determine whether the cost of attending private colleges
is significantly higher than the cost of attending public colleges. Use a = 0.05. A portion of EXCEL
outputs is displayed in the following table.
t-Test: Two-Sample Assuming Unequal
Variances
Private
Public
42.5
22.3
Mean
48.7
20.5
Variance
12
10
Observations
Hypothesized Mean
Difference
df
t Stat
0
15
COC
MacBook Pro

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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