Question

The out-of-state tuitions (in dollars) for random samples of both public and private four-year colleges in a New England state are listed. Find the 95% confidence interval for the difference in the means. Assume the variables are normally distributed and the variances are unequal. Round sample statistics and final answer to two decimal places. Private Public 13,495 12,500 7,050 6,450 23,400 13,326 7,050 7,871 14,291 13,600 9,113 17,760 17,300 16,590 16,100 19,024 14,150 Source: New York Times Almanac. Download Data Use $mu_1$ for the mean out-of-state tuition of private colleges. The 95% confidence interval for the difference of the means is $$$oxed{hspace{1cm}} < mu_1 - mu_2 < oxed{hspace{1cm}}$

          The out-of-state tuitions (in dollars) for random samples of both public and private four-year
colleges in a New England state are listed. Find the 95% confidence interval for the difference in
the means. Assume the variables are normally distributed and the variances are unequal. Round
sample statistics and final answer to two decimal places.
Private
Public
13,495
12,500
7,050
6,450
23,400
13,326
7,050
7,871
14,291
13,600
9,113
17,760
17,300
16,590
16,100
19,024
14,150
Source: New York Times Almanac.
Download Data
Use $mu_1$ for the mean out-of-state tuition of private colleges.
The 95% confidence interval for the difference of the means is
$$$oxed{hspace{1cm}} < mu_1 - mu_2 < oxed{hspace{1cm}}$

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The out-of-state tuitions (in dollars) for random samples of both public and private four-year
colleges in a New England state are listed. Find the 95% confidence interval for the difference in
the means. Assume the variables are normally distributed and the variances are unequal. Round
sample statistics and final answer to two decimal places.
Private
Public
13,495
12,500
7,050
6,450
23,400
13,326
7,050
7,871
14,291
13,600
9,113
17,760
17,300
16,590
16,100
19,024
14,150
Source: New York Times Almanac.
Download Data
Use mu1 for the mean out-of-state tuition of private colleges.
The 95% confidence interval for the difference of the means is

oxedhspace1cm < mu1 - mu2 < oxedhspace1cm

Added by Montserrat Y.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jerelyn Nevil

08/09/2023

Step 1

Private colleges: Sample mean (x̄1) = $15,017.60 Sample standard deviation (s1) = $3,491.67 Sample size (n1) = 10 Public colleges: Sample mean (x̄2) = $9,086.29 Sample standard deviation (s2) = $4,303.47 Sample size (n2) = 7 Show more…

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The out-of-state tuitions (in dollars) for random samples of both public and private four-year colleges in a New England state are listed. Find the 95% confidence interval for the difference in the means. Assume the variables are normally distributed and the variances are unequal. Round sample statistics and final answer to two decimal places. Private 13,495 12,500 23,400 13,326 14,291 13,600 17,300 16,590 19,024 14,150 Public 7,050 6,450 7,050 7,871 9,113 17,760 16,100 Source: New York Times Almanac. Use μ1 for the mean out-of-state tuition of private colleges. The 95% confidence interval for the difference of the means is $____ < μ1 - μ2 < $____.

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00:01 Okay, so i see that you need help with this question, and it says the out -of -state tuition and dollars for random samples of both public and private four -year colleges in new england state are listed.

00:11 Find the 95 % confidence interval for the difference in the means.

00:16 Assume the variables are normally distributed and the variances are equal.

00:20 Round the sample statistics and final answers to two decimal places.

00:27 So let me just get rid of this on the side, so that way i have some more room.

00:36 And for this, the first thing for the public, the mean is going to be 1576 .6, and the standard deviation is going to be 3385 .94.

00:56 And for private, the mean is going to be 10199 .14, and the sample standard deviation is going to be 4698 .88, okay? and the sample size for private is 10, and for public is seven.

01:30 And so the first thing that i have to do is i have to pull their variances.

01:37 So i have to take the degrees of freedom for the private is nine, and for the public is eight.

01:46 So i'm going to take nine times 4698 .88 squared plus, oh, i don't know why i put eight there.

02:04 That should be six.

02:05 Ooh, that should be six.

02:15 So six times 3385 .94 squared, and that is divided by 10 plus seven minus two, and that equals 15710531 .02.

02:35 And so you're gonna take this number, and you're gonna find the square root of that, and that's going to equal 3963 .65...

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