In chapter 5 exercise 9 we studied variability of crime


CHAPTER 8 - Exercise 4

In Chapter 5, Exercise 9, we studied variability of crime rates and police expenditures in the eastern and Midwestern United States. We've now been asked to investigate the hypothesis that the number of crimes is related to police expenditures per capita because states with higher crime rates are likely to increase their police force, thereby spending more on the number of officers on the street.

State

Number of Crimes

Police Protection Expenditures per

Capita (Dollars), per 10,000 People

Maine

2,875

122.5

New Hampshire

2,282

141.8

Vermont

2,819

102.8

Massachusetts

3,262

218.7

Rhode Island

3,583

179.2

Connecticut

3,389

193.6

New York

3,279

292.4

New Jersey

3,400

236.6

Pennsylvania

3,114

171.2

Ohio

3,997

179.4

Indiana

3,766

124.5

Illinois

4,515

224.4

Michigan

4,325

172.3

Wisconsin

3.296

196.6

Minnesota

3,598

166.8

Iowa

3,224

135.8

Missouri

4,578

153.9

North Dakota

2,394

102.9

South Dakota

2,644

115.3

Nebraska

4,108

128.8

Kansas

4,439

161.6

a)      Construct a scatter diagram of the number of crimes and police expenditures per capita, with number of crimes as the predictor variable. What can you say about the relationship between these two variables based on the scatter plot?

b)      Find the least-squares regression equation that predicts police expenditures per capita from the number of crimes. What is the slope? What is the intercept?

c)      Calculate the coefficient of determination (r²), and provide interpretation.

d)     If the number of crimes increased by 100 for a state, by how much would you predict police expenditures per capita to increase?

e)      Does it make sense to predict police expenditures per capita when the number of crimes is equal to zero? Why or why not

CHAPTER 8 - Exercise 8

In Exercise 6, we investigated the relationship between infant mortality rate and GNP in South America. The birth rates (number of live births per 1,000 inhabitants) in these same countries are shown in the following table:

Country

Birth Rate in 1999

GNP per Capita in 1997 ($)

Argentina

19

8,030

Bolivia

32

1,010

Brazil

20

4,630

Chile

18

4,990

Colombia

24

2,740

Ecuador

24

1,520

Paraguay

30

1,760

Peru

25

2,440

Uruguay

17

6,070

Venezuela

25

3,530

a) Construct a scatter plot for GNP and birth rate and one for infant mortality rate and birth rate. Do you think each can be characterized by a linear relationship?

b) Calculate the coefficient of determination and correlation coefficient for each relationship.

Use this information to describe the relationship between the variables.

Solution Preview :

Prepared by a verified Expert
Basic Statistics: In chapter 5 exercise 9 we studied variability of crime
Reference No:- TGS01265488

Now Priced at $30 (50% Discount)

Recommended (96%)

Rated (4.8/5)