# Chi square test and regression analysis problems

Hello,

Attached are 5 statistics problems that I need help. I would like detailed step-by-step guidance to help me better understand the problems. Thanks in advance.

1. To examine the continuity and discontinuity in the criminal careers of 7,453 females of low socio-economic status, Tracy and Kempf-Leonard (1996) examined whether these females were nonoffenders, one-time offenders, recidivist offenders, or chronic offenders as juveniles and adults. Nonoffenders committed zero offenses, one-time offenders committed one offense, recidivist offenders committed two to four offenses, and chronic offenders committed five or more offenses. The following table describes the results:

Juvenile

Offender Group Adult Offender Group

Nonoffender One-Time Recidivist Chronic Total

Nonoffender 5954 149 41 4 6148

One-Time 669 60 13 3 745

Recidivist 385 42 25 3 455

Chronic 73 15 12 5 105

Total 7081 266 91 15 7453

a. What is the probability that an adult is a recidivist offender? P(adult is a recidivist offender)= 91/7453=

b. Is this a conditional or unconditional probability? Explain.

c. What is the probability that an adult is not a recidivist offender?

d. What is the probability that an adult is a recidivist offender or a chronic offender?

e. What is the probability that a juvenile is a nonoffender?

f. What is the probability that a juvenile nonoffender became a chronic offender as an adult?

g. What is the probability that a juvenile's status was not changed into adulthood?

h. What is the probability that a juvenile's status became more severe into adulthood?

2. Let's say that the average salary for a state correctional officer in the United States is equal to $28,250, with a standard deviation of $3,500. Decide which of the following states have unusually high or unusually low salaries, where high and low means in the top or bottom 5%.

a.

b.

c.

d. California

Alaska

New York

Mississippi $23,300

$42,600

$38,800

$15,300

3. Gottfredson et al. (2003) randomly assigned drug offenders to a drug treatment court in Baltimore (MD) or to a regular court. Their hypothesis was that providing drug treatment to these drug offenders is an integral part of their rehabilitation. Offenders who went to drug treatment court, they hypothesized, would be less likely to recidivate in the future. 139 offenders were randomly assigned to the experimental group and 96 offenders were randomly assigned to the control group. The authors performed a process evaluation and an outcome evaluation. In their process evaluation, they wanted to make sure that the drug treatment court actually did provide significantly more treatment than the regular court. 68.3% of the experimental group and 24.0% of the control group received treatment. In their outcome evaluation, they wanted to examine whether the drug treatment court significantly reduced drug-related recidivism. Two years later, 40.6% of the experimental group and 54.2% of the control group were re-arrested with at least one new drug charge. Perform hypothesis tests to determine if the drug treatment court significantly provided more drug treatment and significantly reduced drug-related recidivism. Use a 0.05 level of statistical significance.

4. Braga et al. (1999) examined the effect of problem-oriented policing on loitering. Their hypothesis was that problem-oriented policing would reduce minor incivilities such as loitering. For their experiment, they identified 11 high-crime places in Jersey City (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 researchers also matched these 11 high-crime places to 11 high-crime places that were not assigned to the problem-oriented unit. A traditional enforcement unit that did not engage in problem-oriented policing was selected for these control places. The following table shows the total number of loiterers observed during a 15-minute period in each treatment and control place after the intervention:

Matched Pair Number of Loiterers

In Treatment Place Number of Loiterers in Control Place

1

2

3

4

5

6

7

8

9

10

11 0

11

8

2

5

10

18

15

2

18

4 0

73

23

12

13

26

55

39

7

56

22

Perform a hypothesis test to determine if problem-oriented policing significantly reduced the number of loiterers. Use a 0.05 level of statistical significance.

5. A researcher has studied the relationship between socioeconomic status (SES) and delinquency and age and delinquency. However, now she is interested in studying the relationship between age and socioeconomic status. Both variables have been shown to have a negative relationship with delinquency, but this researcher is interested in finding out more about the relationship between age and SES. She has a set of data in which SES is measured in which a low number indicates low SES. The scores on this measure can range from 0-20. Use the sample of data below to draw a scatterplot, calculate the regression equation, and determine . Is the calculated value significant? Test this using an alpha of 0.01.

Age SES Score

15 3

17 3

18 4

18 6

19 7

23 7

25 8

27 9

30 11

31 13

32 14

33 15

46 17

51 18

62 20

#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems. Step by step method for regression analysis is also discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.