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Education: Violent Crime The following data are based on information from the book Life in America's Small Cities (by G. S. Thomas, Prometheus Books). Let x be the percentage of 16- to 19-year-olds not in school and nothigh school graduates. Let y be the reported violent crimes per 1000 residents. Six small cities in Arkansas (Blythcville, El Dorado. Hot Springs, Jonesboro. Rogers, and Russellville) reported the following information about x and y: x 24.2 19.0 18.2 14.9 19.0 17.5 y 13.0 4.4 9.3 1.3 0.8 3.6 Complete parts (a) through (e). given Σ x = 112.8 , Σ y = 32.4 , Σ x 2 = 2167.14 , Σ y 2 = 290.14 , Σ x y = 665.03 , and r ≈ 0 .764 . (f) If the percentage of 16- to 19-year-olds not in school and not graduates reaches 24% in a similar city, what is the predicted rate of violent crimes per 1000 residents?

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Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075
BuyFind

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075

Solutions

Chapter
Section
Chapter 4.2, Problem 15P
Textbook Problem

Education: Violent Crime The following data are based on information from the book Life in America's Small Cities (by G. S. Thomas, Prometheus Books). Let x be the percentage of 16- to 19-year-olds not in school and nothigh school graduates. Let y be the reported violent crimes per 1000 residents. Six small cities in Arkansas (Blythcville, El Dorado. Hot Springs, Jonesboro. Rogers, and Russellville) reported the following information about x and y:

x 24.2 19.0 18.2 14.9 19.0 17.5
y 13.0 4.4 9.3 1.3 0.8 3.6

Complete parts (a) through (e). given Σ x = 112.8 ,   Σ y = 32.4 ,   Σ x 2 = 2167.14 ,   Σ y 2 = 290.14 ,   Σ x y = 665.03 ,  and  r 0 .764 .

(f) If the percentage of 16- to 19-year-olds not in school and not graduates reaches 24% in a similar city, what is the predicted rate of violent crimes per 1000 residents?

Expert Solution

(a)

To determine

To graph: The scatter diagram.

Explanation of Solution

Given: The data which consists of variables, ‘the percentage of 16 to 19 year olds not in school and not high school graduates’ and ‘the reported violent crimes per 1000 residents’, represented by x and y, respectively is provided.

Graph:

Follow the steps given below in Excel to obtain the scatter diagram of the data.

Step 1: Enter the data into Excel sheet. The screenshot is given below.

Step 2: Select the data and click on ‘Insert’. Go to charts and select the chart type ‘Scatter’...

Expert Solution

(b)

To determine

To test: Whether the provided values of x, y, x2 ,y2, xy and r are correct or not.

Expert Solution

(c)

To determine

To find: The values of x¯,y¯, a, b and the equation for the least-squares line.

Expert Solution

(d)

To determine

To graph: The least-squares line on the scatter diagram which passes through the point (x¯,y¯).

Expert Solution

(e)

To determine

The value of r2, the percentage of variation that can be explained and the percentage of variation that is unexplained.

Expert Solution

(f)

To determine

To find: The predicted rate of violent crimes per 1000 residents.

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Chapter 4 Solutions

Understanding Basic Statistics
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