Data Analysis Sample T-tests/Introduction to CJ Data Analysis

The United States Department of Justice has commissioned an investigation into the way police departments, in the United States, handle citizens’ calls for service. The investigation is a response to an allegation that police are unusually more responsive to calls in non-inner city areas. The police, in turn, are alleging that their poor response rate in inner-city areas is not a result of police bias. Rather, it is the consequence of the fact that, on the average, inner city folks inundate the police with so many calls, the police simply do not have enough resources to respond to all the calls in a timely fashion. Below are the average numbers of calls to police, per month, from a stratified sample of communities across America over a 13-month period.

Inner-City Suburban Urban Rural

4 0 7 0

0 7 8 0

8 6 9 5

12 4 11 1

24 12 1 3

52 52 5 2

10 8 0 4

14 18 0 6

87 24 4 0

30 1 6 1

2 6 3 3

1 5 8 4

18 10 1 6

1. What are the null and alternative hypotheses for this experiment?

2. Is the experiment a one-tail or two-tail test? Explain your choice

3. What is the level of significance of this test (set p=0.01)?

4. How many degrees of freedom are there?

5. What is the critical value of the F- statistic?

6. Draw a normal curve, input the critical value on the normal curve you have drawn, and shade the rejection region

7. Compute the F-statistic.

8. Comparing the F-statistic to your critical value, should we reject the null hypothesis? Why or why not?

9. Does area of residence affect the frequency of calls to police?

Question #2

A researcher wishes to examine the effect of problem-oriented policing on incivilities. Her hypothesis was that problem-oriented policing would reduce minor incivilities such as loitering. For the experiment, she identified 11 high-crime places in Trenton (NJ) and assigned them to a problem-oriented policing unit. This unit was asked to analyze the problem in each area and to create an effective response to it. The following table shows the data before and after the intervention:

Number of Loiterers

Before Intervention Number of Loiterers After Intervention

21

11

8

2

15

10

18

15

2

18

14 10

73

23

12

13

26

55

39

17

56

22

Perform a hypothesis test to determine if problem-oriented policing significantly reduced the number of loiterers.

a. What are the null and alternative hypotheses for this experiment?

b. Is the test one-tail or two-tail? Explain your choice

c. What is the level of significance of this test? (use p=0.05)

d. How many degrees of freedom are there?

e. What is the critical value of t?

f. Draw a normal curve, enter the critical value on the normal curve you have just drawn, and shade the rejection region

g. Compute the t- statistic

h. Enter the t-value you have just computed on the normal curve you drew in (f)

i. Should we reject the null hypothesis? Why or why not?

j. What should be the conclusion for this research?

Data Analysis Sample T-tests/Introduction to CJ Data Analysis

The United States Department of Justice has commissioned an investigation into the way police departments, in the United States, handle citizens’ calls for service. The investigation is a response to an allegation that police are unusually more responsive to calls in non-inner city areas. The police, in turn, are alleging that their poor response rate in inner-city areas is not a result of police bias. Rather, it is the consequence of the fact that, on the average, inner city folks inundate the police with so many calls, the police simply do not have enough resources to respond to all the calls in a timely fashion. Below are the average numbers of calls to police, per month, from a stratified sample of communities across America over a 13-month period.

Inner-City Suburban Urban Rural

4 0 7 0

0 7 8 0

8 6 9 5

12 4 11 1

24 12 1 3

52 52 5 2

10 8 0 4

14 18 0 6

87 24 4 0

30 1 6 1

2 6 3 3

1 5 8 4

18 10 1 6

1. What are the null and alternative hypotheses for this experiment?

2. Is the experiment a one-tail or two-tail test? Explain your choice

3. What is the level of significance of this test (set p=0.01)?

4. How many degrees of freedom are there?

5. What is the critical value of the F- statistic?

6. Draw a normal curve, input the critical value on the normal curve you have drawn, and shade the rejection region

7. Compute the F-statistic.

8. Comparing the F-statistic to your critical value, should we reject the null hypothesis? Why or why not?

9. Does area of residence affect the frequency of calls to police?

Question #2

A researcher wishes to examine the effect of problem-oriented policing on incivilities. Her hypothesis was that problem-oriented policing would reduce minor incivilities such as loitering. For the experiment, she identified 11 high-crime places in Trenton (NJ) and assigned them to a problem-oriented policing unit. This unit was asked to analyze the problem in each area and to create an effective response to it. The following table shows the data before and after the intervention:

Number of Loiterers

Before Intervention Number of Loiterers After Intervention

21

11

8

2

15

10

18

15

2

18

14 10

73

23

12

13

26

55

39

17

56

22

Perform a hypothesis test to determine if problem-oriented policing significantly reduced the number of loiterers.

a. What are the null and alternative hypotheses for this experiment?

b. Is the test one-tail or two-tail? Explain your choice

c. What is the level of significance of this test? (use p=0.05)

d. How many degrees of freedom are there?

e. What is the critical value of t?

f. Draw a normal curve, enter the critical value on the normal curve you have just drawn, and shade the rejection region

g. Compute the t- statistic

h. Enter the t-value you have just computed on the normal curve you drew in (f)

i. Should we reject the null hypothesis? Why or why not?

j. What should be the conclusion for this research?