Question

The increasing annual cost (including tuition, room, board, books and fees) to attend college has been widely discussed in many publications including Money magazine. 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 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places. b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place. B. interpret this value in terms of the annual cost of attending private and public colleges. $__ c. Develop a 95% confidence interval of the difference between the mean annual cost of attending private and public colleges. 95% confidence interval, private colleges have a population mean annual cost $_ to $____ more expensive than public colleges.

          The increasing annual cost (including tuition, room, board,
books and fees) to attend college has been
widely discussed in many publications
including Money magazine. 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
a. Compute the sample mean and sample
standard deviation for private and public colleges. Round your
answers to two decimal places.
b. What is the point estimate of the
difference between the two population means? Round your answer to
one decimal place.
           B. interpret this value
in terms of the annual cost of attending private and public
colleges. $____
c. Develop a 95% confidence interval of
the difference between the mean annual cost of attending private
and public colleges.
               95%
confidence interval, private colleges have a population mean annual
cost $___  to $____ more expensive than public colleges.

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Added by Gregory B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Elias Robbins

05/16/2022

Step 1

For private colleges, the sample mean is calculated by adding all the values and dividing by the number of values. The sample standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences from the Show more…

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The increasing annual cost (including tuition, room, board, books and fees) to attend college has been widely discussed in many publications including Money magazine. 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 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places. b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place. B. interpret this value in terms of the annual cost of attending private and public colleges. $____ c. Develop a 95% confidence interval of the difference between the mean annual cost of attending private and public colleges. 95% confidence interval, private colleges have a population mean annual cost $___ to $____ more expensive than public colleges.

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Transcript

00:01 Hey guys, this problem's pretty long, so i've already written some stuff out, but i'm going to explain it i've really just written down the for private and for public costs and your mean and standard deviation formula is right here.

00:14 I'm just going to highlight them.

00:16 I've already done out one sample calculation, or at least written it out.

00:21 So that's how you do mean, and then the standard deviation is just the sum of your given numbers minus your mean and then divided by the number of samples, square root that, and that gets you your standard.

00:31 So for the mean for the private, it ends up being, and i'm going to write this in blue so you can see it better.

00:39 40, oh, that's not blue, 42 .5.

00:45 Your mean for public, i've already done all the math out to save time, but your mean for public is 22 .3.

00:55 For standard deviation following this formula, right here you get for private schools, for 0 .53 and then for public schools it's 6 .98.

01:11 All right so for the point estimate it's really just looking for what's the difference between the means.

01:17 So you do the mean of private minus the mean of public.

01:22 So 42 .5 minus 22 .3 and you get 20 .2.

01:30 Now to explain this, i won't write it.

01:32 I'll just explain it.

01:32 And this pretty much just means that the average of private schools, the average cost of private schools is 20 .2 ,000 more than the average cost of public schools.

01:45 Okay, for the confidence interval part, first you need to calculate the degrees of freedom of the sample.

01:55 I wrote out the formula and filled it in already...

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