In: Statistics and Probability

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 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 52.8 43.2 45.0 33.3 44.0 30.6 45.8 37.8 50.5 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 Using manual calculation to answer the following questions:

a. Compute the sample mean and the sample standard deviation for private and public collages

b. What is the point estimate of the difference between the population mean?

c. Interpret this value in terms of the annual cost of attending private and public colleges.

d. Develop a 95% confidence interval of the difference between the mean annual cost of attending private and public colleges.

(a)

Private colleges: x-bar = 42.5, s = 6.9806

Public colleges: x-bar = 22.3, s = 4.5323

(b)

Point estimate = 42.5 - 22.3 = 20.2

(c)

On average, there is a difference of about $20200 dollars in cost between attending a public college and a private college

(d)

n1 = 10

n2 = 12

x1-bar = 42.5

x2-bar = 22.3

s1 = 6.9806

s2 = 4.5323

% = 95

Degrees of freedom = n1 + n2 - 2 = 10 + 12 -2 = 20

Pooled s = √(((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = √(((10 - 1) * 6.9806^2 + ( 12 - 1) * 4.5323^2)/(10 + 12 -2)) = 5.764191892

SE = Pooled s * √((1/n1) + (1/n2)) = 5.76419189232107 * √((1/10) + (1/12)) = 2.468079516

t- score = 2.085963441

Width of the confidence interval = t * SE = 2.08596344129554 * 2.468079516164 = 5.148323641

Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = 20.2 - 5.1483236409285 = 15.05167636

Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = 20.2 + 5.1483236409285 = 25.34832364

The confidence interval is [15.05, 25.35], that is [$15052, $25348]

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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
53.8
44.2
45.0
32.3
44.0
29.6
46.8
37.8
50.5
42.0...

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
51.8
44.2
45.0
34.3
45.0
31.6
46.8
36.8
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
(a)
Compute the sample mean (in thousand dollars) and sample
standard deviation (in thousand dollars)...

The
average undergraduate cost for tuition, fees, and room and board
for two-year institutions last year was $13,252. The following
year, a random sample of 20 two-year institutions had a mean of
$15,560 and a standard deviation of $3500. Is there sufficient
evidence at the ?= 0.05 level to conclude that the mean cost has
increased. Solve the question by traditional approach.
Question no 2: A large university reports that the mean salary
of parents of an entering class is...

The average cost of tuition and room and board for a small
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a financial administrator believes that the average cost is higher.
A study conducted using 350 small liberal arts colleges showed that
the average cost per term is $8,745. The population standard
deviation is $1,200. Let α = 0.05. What are the null and
alternative hypotheses for this study? rev: 06_20_2017_QC_CS-91792
Multiple Choice H0: µ ≤ $9,000;...

(10) The average tuition and room and board cost at a small
private liberal arts college is reported to be $20,000 per term. A
study of 400 small liberal arts colleges find that the average cost
per term is $20,100. The population standard deviation is $1,500.
If α = 0.05, what is the critical Z value for the test: Ho: µ=
20,000?

The mean undergraduate cost for tuition, fees, room, and board
for four-year institutions was $26,489 for a recent academic year.
Suppose that that LaTeX: \sigmaσ =$3204 and that 36 four-year
institutions are randomly selected. Find the probability that the
sample mean cost for these 36 schools is
a) Less than $25,000 P(x(bar) < 25000)= , Calcuator part
Answer= , round your answer to 4 decimal places
b) Greater than $26,000 P(x(bar) > 26000)= , Calcuator
part
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A financial administrator believes the average cost of tuition
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per term. A study conducted using 350 small liberal arts colleges
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0.0500
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The average cost of tuition, room and board at small private
liberal arts colleges is reported to be $8,500 per term, but a
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different. A study conducted using 50 small liberal arts colleges
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$20,598. In 2018, the average annual tuition for a public
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