Question

Annual cost of College. 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. $$ \begin{aligned} &\text { Private Colleges }\\ &\begin{array}{lllll} 52.8 & 43.2 & 45.0 & 33.3 & 44.0 \\ 30.6 & 45.8 & 37.8 & 50.5 & 42.0 \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { Public Colleges }\\ &\begin{array}{llllll} 20.3 & 22.0 & 28.2 & 15.6 & 24.1 & 28.5 \\ 22.8 & 25.8 & 18.5 & 25.6 & 14.4 & 21.8 \end{array} \end{aligned} $$ a. Compute the sample mean and sample standard deviation for private and public colleges. b. What is the point estimate of the difference between the two population means? 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.

          Annual cost of College. 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.
$$
\begin{aligned}
&\text { Private Colleges }\\
&\begin{array}{lllll}
52.8 & 43.2 & 45.0 & 33.3 & 44.0 \\
30.6 & 45.8 & 37.8 & 50.5 & 42.0
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\text { Public Colleges }\\
&\begin{array}{llllll}
20.3 & 22.0 & 28.2 & 15.6 & 24.1 & 28.5 \\
22.8 & 25.8 & 18.5 & 25.6 & 14.4 & 21.8
\end{array}
\end{aligned}
$$
a. Compute the sample mean and sample standard deviation for private and public colleges.
b. What is the point estimate of the difference between the two population means? 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.

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Added by Michael N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jerelyn Nevil

08/04/2023

Step 1

Private Colleges: Mean: $\bar{x}_1 = \frac{52.8 + 43.2 + 45.0 + 33.3 + 44.0 + 30.6 + 45.8 + 37.8 + 50.5 + 42.0}{10} = 42.5$ Standard Deviation: $s_1 = \sqrt{\frac{(52.8-42.5)^2 + \cdots + (42.0-42.5)^2}{10-1}} \approx 6.77$ Public Colleges: Mean: $\bar{x}_2 = Show more…

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Annual cost of College. 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. $$ egin{aligned} & ext { Private Colleges }\ &egin{array}{lllll} 52.8 & 43.2 & 45.0 & 33.3 & 44.0 \ 30.6 & 45.8 & 37.8 & 50.5 & 42.0 end{array} end{aligned} $$ $$ egin{aligned} & ext { Public Colleges }\ &egin{array}{llllll} 20.3 & 22.0 & 28.2 & 15.6 & 24.1 & 28.5 \ 22.8 & 25.8 & 18.5 & 25.6 & 14.4 & 21.8 end{array} end{aligned} $$ a. Compute the sample mean and sample standard deviation for private and public colleges. b. What is the point estimate of the difference between the two population means? 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.

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00:01 Okay, so i see that you need help with this question, and so it says annual cost of college.

00:05 The increasing annual cost, including tuition, room, board, books, and fees to attend college has been widely discussed in many publications, including money magazine.

00:16 The following random samples show the annual cost of attending private and public colleges.

00:22 Data are in the thousands of dollars.

00:24 Compute the sample mean and sample standard deviation of private and public colleges.

00:29 So for the private colleges, the amount of numbers that are here is two, four, six, eight, 10.

00:41 The mean is 42 .5.

00:47 The standard deviation is 6 .98.

00:54 For the public colleges, there's a total of 12 numbers.

01:04 The mean is 22 .3, and the standard deviation is 4 .53.

01:15 What is the point estimate of the difference between the two population means? so this was a, and then b, the point estimate for the difference between the two population means.

01:27 So you're gonna take 42 .5 minus 22 .3, and that is 20 .2, and it says develop a 95 % confidence interval for the difference between the mean annual cost of attending private and public colleges.

01:50 So what you're going to do is you first need to pool the variances.

01:55 So you're gonna take your degrees of freedom for the private, which is 10 minus one, and that's nine...

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