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You may need to use the appropriate appendix table or technology to answer this question. 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 Private Colleges Public Colleges 51.8 44.2 46.0 33.3 43.0 20.3 22.0 28.2 15.6 24.1 22.8 25.8 18.5 25.6 14.4 21.8 31.6 44.8 37.8 50.5 41.0 (a) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.) sample mean $ 42.4 ✓thousand sample standard deviation $ 6.66 ✔ thousand Compute the sample mean sample mean sample standard deviation $4.53 24.1 28.5 (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.) $ 22.3 thousand thousand ✓ ✔ (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private Public.) $ 20.100 ✔ thousand Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges. We estimate that the mean annual cost to attend private colleges is $ 20.10 x more than the mean annual cost to attend public college (c) Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private Public. Round your answers to one decimal place.) $ 15.0 x thousand to $ 25. x thousand

You may need to use the appropriate appendix table or technology to answer this question. 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 Private Colleges Public Colleges 51.8 44.2 46.0 33.3 43.0 20.3 22.0 28.2 15.6 24.1 22.8 25.8 18.5 25.6 14.4 21.8 31.6 44.8 37.8 50.5 41.0 (a) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.) sample mean $ 42.4 ✓thousand sample standard deviation $ 6.66 ✔ thousand Compute the sample mean sample mean sample standard deviation $4.53 24.1 28.5 (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.) $ 22.3 thousand thousand ✓ ✔ (b) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private Public.) $ 20.100 ✔ thousand Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges. We estimate that the mean annual cost to attend private colleges is $ 20.10 x more than the mean annual cost to attend public college (c) Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private Public. Round your answers to one decimal place.) $ 15.0 x thousand to $ 25. x thousand

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 costs of attending private and public colleges: - **Private Colleges** (in thousand dollars): - Sample Data: 51.8, 44.2, 46.0, 33.3, 43.0 - Computations: - Sample Mean: 42.4 thousand - Sample Standard Deviation: 6.66 thousand - **Public Colleges** (in thousand dollars): - Sample Data: 20.3, 22.0, 28.2, 15.6, 24.1, 28.5 - Computations: - Sample Mean: 22.3 thousand - Sample Standard Deviation: 4.53 thousand ### Analysis: (a) **Comparison of Sample Data:** - Private colleges have a higher average annual cost than public colleges, reflected in the means and standard deviations. (b) **Point Estimate of Difference:** - The point estimate of the difference between the two population means (Private - Public) is calculated as 20.100 thousand dollars. - Interpretation: The mean annual cost to attend private colleges is estimated to be $20.10 thousand more than that for public colleges. (c) **Confidence Interval:** - A 95% confidence interval for the difference between the mean annual costs is calculated from $15.0 thousand to $25.5 thousand, indicating a range in which the true cost difference likely falls. The data supports discussions about the significant cost difference between private and public college attendance, highlighting financial considerations for prospective students.
Transcribed Image Text: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 costs of attending private and public colleges: - **Private Colleges** (in thousand dollars): - Sample Data: 51.8, 44.2, 46.0, 33.3, 43.0 - Computations: - Sample Mean: 42.4 thousand - Sample Standard Deviation: 6.66 thousand - **Public Colleges** (in thousand dollars): - Sample Data: 20.3, 22.0, 28.2, 15.6, 24.1, 28.5 - Computations: - Sample Mean: 22.3 thousand - Sample Standard Deviation: 4.53 thousand ### Analysis: (a) **Comparison of Sample Data:** - Private colleges have a higher average annual cost than public colleges, reflected in the means and standard deviations. (b) **Point Estimate of Difference:** - The point estimate of the difference between the two population means (Private - Public) is calculated as 20.100 thousand dollars. - Interpretation: The mean annual cost to attend private colleges is estimated to be $20.10 thousand more than that for public colleges. (c) **Confidence Interval:** - A 95% confidence interval for the difference between the mean annual costs is calculated from $15.0 thousand to $25.5 thousand, indicating a range in which the true cost difference likely falls. The data supports discussions about the significant cost difference between private and public college attendance, highlighting financial considerations for prospective students.
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