study.sagepub.com · Web viewWe take a random sample of 50 inmates currently convicted and incarcerated for aggravated assault, their sentence lengths are reported below. Stated Limits

Instructor ResourcePaternoster, Essentials of Statistics for Criminology and Criminal Justice

SAGE Publishing, 2018

Chapter Test Problems1. For each of the following statements, write which one is the independent and which is the dependent variable.

a. You think there is a relationship between the age at which someone was first arrested and the number of arrests they have after age 18.

Independent variable ____________

Dependent variable ____________

b. You think there is a relationship between someone’s race/ethnicity and the length of their prison sentence.



c. You think there is a relationship between the arrest record that the parent has and the number of delinquent offenses committed by the eldest child.



d. You think there is a relationship between how quickly the police in your town respond to a 911 call and the social class of the neighborhood where the call came from.



2. What is the level of measurement for each of the following variables?

a. The number of drunk driving arrests for a person measured as______ times (the exact number of times)

______ level



b. The number of drunk driving arrests for a person measured as0–2 times ______3–5 times ______6–8 times ______9 or more times ______

______ level

c. The type of counsel at trial someone hadRetained counsel (paid for it themselves) ______Public defender ______No counsel at trial ______

______ level

3. We are examining sentence lengths in months for people convicted of aggravated assault in Maryland. We take a random sample of 50 inmates currently convicted and incarcerated for aggravated assault, their sentence lengths are reported below.

Stated Limits Real Limits f cf % c%

m fm m2 fm2

1–6 .5 – 6.5 7 7 14 14 3.5 24.5 12.25 85.75

7– 12 6.5–12.5 12 19 24 38 9.5 114.0

90.25 1083.00

13– 18 12.5–18.5 7 26 14 52 15.5 108.5

240.25 1681.75

19– 24 9 35 18 193.5

462.25 4160.25

25– 30 5 137.5

756.25 3781.25

31– 36 7 234.5

1122.25

7855.75

37– 42 3 118.5

1560.25

4680.75

Σ 50 931. 4243.7 23,328.5



0 5 0

a. In the chart above, fill out the columns for real limits, cumulative frequency, percentage, cumulative percentage, and midpoint.

b. What is the modal sentence length?

c. Calculate and interpret the median.

d. Calculate and interpret the mean.

e. Calculate the standard deviation and variance.

f. What percentage of the offenders received a sentence length of 2 years or less?

g. How many, and what proportion of the offenders received a sentence of 19 months or more?

4. The number of thefts and the median sentence lengths (in months) for theft in the state of Maryland for 5 years is reported below.

Year Number of Thefts Population Theft Rate per 10,000

1990

5,782 4,803,550

199 7,898 5,670,627



5

2000

8,024 5,690,703

2005

4,153 5,500,875

2010

6,907 5,876,519

a. Why would it be inappropriate to directly compare the raw number of thefts for each year?

b. Calculate the rates of theft per 10,000 for each year.

c. What was the percentage change in the number of thefts from 2000 to 2005?

d. What was the percent change in the number of thefts from 1990 to 2010?

5. Below is the actual number of thefts caught on security cameras in a random sample of 27 department stores in D.C. over the past year. The empty columns are to aid you in your calculations for the remainder of the problem.

x f p cf cp fx x2 fx2

1 3 .11 3 .11 3 1 3

2 7 .26 10 .37 14 4 28

3 2 .07 12 .44 6 9 18

5 10 22 50 25 250

6 3 .11 18 36 108

12 2 24 144

288



Σ 27 115 219

695

a. Fill out the labeled columns.

b. What is our level of measurement for thefts?

c. What was the modal number of thefts?

d. Calculate and interpret the mean number of thefts caught on security cameras.

e. Calculate and interpret the median number of thefts.

f. What is the range of the number of thefts?

g. Calculate the variance.

h. Calculate and interpret the standard deviation of the number of thefts caught on security cameras.

6. The following data represents the responses of 1,000 citizens of South Park to the question, “How satisfied are you with police services provided by the South Park Police Department?”

fVery Unsatisfied 128Unsatisfied 216Satisfied 485Very Satisfied 171

a. What is the level of measurement? ____________



b. Determine, calculate, and interpret the appropriate measure of central tendency. Mode is Satisfied

c. Determine, calculate, and interpret the appropriate measure of dispersion.

d. What percentage of the residents were either Satisfied or Very Satisfied with the police services of South Park Police Department?

e. Graph the percent data.

7. Social control theory argues that individuals with strong ties to conventional institutions will tend to commit fewer criminal acts. The following contingency table presents information regarding the strength of conventional ties and number of criminal acts for 89 individuals. Use this information to answer the following probability questions:

a. What is the probability that someone has strong conventional ties?

b. What is the probability that someone has committed more than 5 criminal acts?

c. What is the probability that someone had 5 or less criminal acts?

d. What is the probability that someone had weak ties or 3 to 5 criminal acts? Are these mutually exclusive events? Explain.

e. What is the conditional probability that someone had 6 or more criminal acts given that they had strong ties?

f. What is the probability that someone had weak ties and 0–2 criminal acts?

e. Are conventional ties and criminal acts statistically independent or statistically dependent? Explain.



f. What is the probability that someone did not have strong ties and did not commit 6 or more criminal acts?

8. You are the colonel of the Maryland State Police, and you are concerned about drinking among state troopers. You take a random sample of 150 police offers and find that the median number of drinks per week is 2 per week and the mean number of drinks per week is 4.7 with a standard deviation of 8.

a. Is your sample skewed, how can you tell, and if so, in what direction?

b. Construct a 90% confidence interval around the appropriate point estimate. Interpret your results.

c. Construct a 93% confidence interval around your point estimate. Interpret your results. Why did the interval change?

d. What would happen if we increased our confidence level to 99% (You do not need to recalculate the c.i.)?

e. What would happen to the size of your 90% confidence interval if you increased your sample size from 150 to 500? (You do not need to recalculate the c.i.).

f. Recalculate a 90% confidence interval but assume that now you only have a sample size of 16 officers (your sample standard deviation is still 8). Interpret this new interval and explain why it is different from the 90% confidence interval you calculated in part b above? Be specific.

9. You want to estimate the proportion of adults in your state who think that existing gun laws are too weak and should be made stricter to include full background checks, a 30-day waiting period and other things. You take a sample of 250 people in your state and find that 183 of them are in favor of making gun laws stricter.

a. What is your point estimate of the proportion of adults in your state who favor stricter gun laws?

b. Build a 95% confidence interval around your point estimate and interpret your results.

c. Build a 99% confidence interval around your point estimate. What happens to the size of the interval and why? Can you explain this?

10. According to the Gallup Polling Organization, 46% of the U.S. population thinks that the criminal justice (CJ) system is too lenient. You take a sample of 200 University of Maryland students and find that 80 of them think that the criminal justice system is too lenient.



a. Construct a 95% confidence interval around your point estimate.

b. In a hypothesis test, where the null hypothesis is that the percentage of Maryland students who think that the CJ system is too lenient, is no different than the national average; the alternative hypothesis is that Maryland students are different than the national average. Based on the results from your confidence interval above (i.e., with an alpha of .05), would you reject or fail to reject the null hypothesis? You DO NOT need to do the steps of the test . . .

c. What would happen to the size of your interval if you increased your confidence from 95% to 99%?

d. What would happen to the size of your 95% confidence interval if you increased your sample size from 200 to 500?

e. What would happen to the size of your 95% confidence interval if you decreased your sample size from 200 to 50?

11. Your job as the research director in the Maryland Department of Youth Services is to advise the Director which policies to follow. In the past, you have heard that some institutions have had as many as 80 disturbances in a year. The average number of disturbances (riots, stabbings, fights, etc.) per year per institution, though, is 35, with a standard deviation of 7.0. The distribution is normal. Answer the following questions:

a. What is the z score for an institution that had 28 disturbances in 1 year? What does this z score indicate?

b. What is the z score for an institution that had 45 disturbances in 1 year?

c. You want to give raises to the wardens in the prisons that have disturbances in the bottom 10% of the distribution, and fire the wardens in prisons in the top 5%. What number of disturbances will be the cutoff for each of these decisions?

d. What is the probability that an institution would have 40 or more disturbances?

e. What is the probability that an institution would have 32 or fewer disturbances?

f. Suppose the director wanted to identify the top 20% of institutions for reprimand. How many disturbances would qualify as the cutoff?

g. Suppose the director wanted to identify the bottom 5% of institutions for praise. How many disturbances would qualify as the cutoff?



12. Suppose you take a sample of 81 offenders from Maryland state prisons and you find that the average number of tattoos is 4.4 with a standard deviation of 1.9. According to Tattoo Me magazine, the average number of tattoos for all incarcerated offenders is 2.9.

a. Test the null hypothesis that Maryland offenders have the same mean number of tattoos as other offenders in the general incarcerated population against the alternative that they have a significantly different mean number of tattoos. Use an alpha level of .05. Interpret your results.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

b. Suppose your sample size was only 40 prisoners. Can you still conclude that there is a significant difference in the mean number of tattoos? Conduct the appropriate hypothesis test to answer this question. Interpret your results.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

c. You take a new sample of 100 prisoners who have tattoos and find that 42% of their tattoos are located on their arms. Tattoo Me magazine reports that 38% of all individuals with tattoos have them on their arms. Is the proportion of tattoos on prisoners’ arms significantly greater than the proportion in the general public? Using an alpha of .01, conduct a hypothesis test to answer this question. Interpret your results.

Step 1:

Step 2:

Step 3:



Step 4:

Step 5:

13. You are interested in examining if the gender of the offender is related to whether or not armed robbers are arrested. You know that the overall probability of arrest for armed robbers is .7. You obtain a random sample of 10 female armed robbers and observe that only two of them were arrested. Assuming we can use a binomial to answer this question, calculate the probability of observing exactly two arrests out of 10 robberies in your data.

14. There has been a lot of talk about the “gang gene” in criminology and the national news lately. The gang gene is a particular gene called MAOA and males with it are supposed to be at high risk of being violent, including members of a gang. You take a random sample of 1,000 residents of a neighborhood in Compton, California, and test for the presence of both the MAOA gene and whether or not there is evidence that the person has been or is currently a gang member.

Here are the data you get as your Observed Frequencies:

Not in a Gang In a Gang TotalHas MAOA Gene 416 384 800No MAOA Gene 110 90 200

Total 526 474 1,000

Here are your Expected Frequencies under the assumption of independence:

Not in a Gang In a Gang TotalHas MAOA Gene 421 379 800No MAOA Gene 105 95 200

Total 526 474 1,000

a. What is the independent variable here and what is the dependent variable?

b. What is the probability that someone is a member of a gang?

c. What is the relative risk of gang membership for those without and with the MAOA gene?



d. Test the null hypothesis that the MAOA gene and gang membership are independent from each other against the alternative that they are dependent or that there is an association between them. Use an alpha of .05 and state each step of your hypothesis test. Step 1:

Step 2:

Step 3:

Step 4:

Step 5: What do you conclude? Explain.

e. Calculate and interpret the strength of the relationship between the MAOA gene and gang membership? Should we conclude that all the hype about the gang gene is supported by the facts?

15. Do first time offenders who are sent to prison earn less money from legal work after release than first time offenders who were given probation? To test this idea, you take a random sample of 125 first time offenders who were sent to prison after conviction. In the year after they were released, the average amount of money they earned in legal work was $12,800, with a standard deviation of $1,100. You take a second independent sample of 90 first time offenders who received probation after conviction. In the year after they were released, the average amount of money they earned in legal work was $14,600 with a standard deviation of $500. Test the null hypothesis that those sent to prison earn the same amount of money after release as those given probation against the alternative that they earn less. Use an alpha of .05 and state each step of your hypothesis test. What is your conclusion? In your hypothesis test, you cannot assume that the population standard deviations are equal (σ1 ≠ σ2). Assume that you have 120 degrees of freedom.



a. What is the independent variable?

b. What is the dependent variable?

c. Test the null hypothesis that those sent to prison earn the same amount of money after release as those given probation against the alternative that they earn less. Use an alpha of .05 and state each step of your hypothesis test. What is your conclusion? In your hypothesis test, you cannot assume that the population standard deviations are equal (σ1 ≠ σ2). Assume that you have 120 degrees of freedom.

STEP 1:

STEP 2:

STEP 3:

STEP 4:

STEP 5:

16. It has always been claimed that being unemployed puts you at higher risk of committing a crime. To investigate this possibility you examine the relationship between being unemployed in the past year and being arrested. Here’s the data that you get:

OBSERVED FREQUENCIES



Employed Unemployed TotalNo Arrest 65 25 90

One or MoreArrests

35 45 80

Total 100 70 170



c. What is the unconditional risk of having one or more arrests?

d. What is the relative risk of having one or more arrests for those who were employed in the past year?

e. What is the relative risk of having one or more arrests for those who were unemployed in the past year?

f. Are the events of employment and arrest independent events? Explain.

g. Test the null hypothesis that employment/unemployment in the past year and arrest are independent against the alternative hypothesis that they are dependent or are related to one another. Use an alpha of .01 and state each step of your hypothesis test. What is your decision and what do you conclude? To help you out, I have provided you with the table of expected frequencies below.

STEP 1:

STEP 2:

STEP 3:

STEP 4:

STEP 5:

h. Calculate an appropriate measure of association and describe the strength of the relationship between (if any) between unemployment and crime.

17. One of the complaints about immigration in the United States is that immigrants are more criminal than those who are natives. This, of course, is an empirical question, so you go to Arizona and take a random sample of 61 illegal immigrants from Mexico (from a group of immigrants detained by INS) and a second independent random sample of 61 persons in the same area who are not immigrants. For each person in both samples, you do a records check to



see how many arrests they have had in the past (both in the U.S. and Mexico) and calculate the average number of arrests in each group. Here’s the data you obtained:



c. Test the null hypothesis that the mean number of arrests for illegal immigrants is no different from that for non-immigrants, against the alternative hypothesis that the average number of arrests for immigrants is greater than that for non-immigrants. Use an alpha of .01. You may assume that the population standard deviations are equal (σ1 = σ2). State each step of your hypothesis test. What is the conclusion that you would draw about crime between immigrants and non-immigrants?

STEP 1:

STEP 2:

STEP 3:

STEP 4:

STEP 5:

18. As the instructor, I am interested in whether or not students who fail this statistics course one semester do better on their exams the second time they take the class. To examine this, I record the exam scores for a sample of 10 students who took the class last semester and are repeating the class this semester. The exam scores for these 10 students are reported below for last semester and this semester. Alpha = .05.



a. What are the independent and dependent variables and their levels of measurement?

b. Conduct the appropriate hypothesis test to determine whether or not student scores are significantly greater for students taking the class the second semester compared to their scores the first semester. State each step of the test and interpret your results.

Student Semester 1 Semester 2x1 x2

A 65 78B 70 72C 54 66D 66 57E 42 50F 69 82G 70 70H 64 62I 39 55J 53 60

Σ

19. You want to investigate whether or not children who have parents with criminal records are more likely to get in trouble with the law than children who have parents with no criminal record. You take a sample of 50 children who have at least one parent who has been convicted of a crime, and you take a separate sample of 100 children whose parents have never been convicted of a crime. You find that 44% of the sample of children with criminal parents have been in trouble with the law whereas 39% of the sample of children with non-criminal parents have been in trouble with the law.

a. What are the independent and dependent variables and their levels of measurement?

b. Conduct the appropriate hypothesis test to see if there is a significant difference in the proportion of children who have been in trouble with the law between the two groups. State the steps of your test and interpret your results. Alpha = .05.

20. As the head of research for the Probation Department of Bikini Bottom, you want to know if reducing the caseload size of your probation officers will result in better care and therefore fewer new arrests for those on probation. You compare the number of arrests for probationers who are in one of four groups:



1. Low-case load (less than 25 probationers)2. Middle-low case load (between 25 and 49 probationers)3. Middle-high case load (between 50 and 74 probationers)4. Large case load (between 75 and 100 probationers)

You have eight probationers in each group.a. What is the independent variable and what are the values of that variable?


c. Test the null hypothesis that the mean number of offenses in the four groups is the same (µ1 = µ2 = µ3 = µ4) against the alternative that they are different (µ1 ≠ µ2 ≠ µ3 ≠ µ4), use an alpha of .05. State each step of your hypothesis test. What would you conclude and more importantly? The data are below:

Group Number of Arrests

1.0 2.001.0 1.001.0 2.001.0 .001.0 2.001.0 1.001.0 1.001.0 2.00

2.0 3.002.0 2.002.0 3.002.0 1.002.0 1.002.0 .002.0 .002.0 3.00

3.0 4.003.0 5.003.0 6.003.0 5.003.0 7.003.0 7.003.0 8.003.0 6.00



4.0 6.004.0 5.004.0 7.004.0 8.004.0 5.004.0 6.004.0 9.004.0 5.00

d. If the critical difference from Tukey’s HSD test was 2.5, which pair of means would be different from each other? Based upon this, what is the optimal number of probationers you would assign to each probation officer based on your analysis?

e. What is the strength of the relationship between caseload size and number of arrests? Explain and calculate the relevant statistic.

21. You think that a Head Start program for kids will reduce their risk of later getting involved in delinquency. To test this idea you take a sample of 95 homes where the child had been enrolled in Head Start and 125 homes in the same neighborhood where the child had not been enrolled in Head Start. You find that by age 18, 25 of the kids who had been in Head Start had at some time been arrested and sent to the juvenile court while 55 of the kids who had not been in Head Start had an arrest and juvenile court record by age 18. Test the null hypothesis that being in Head Start has no effect on the proportion of kids who end up being delinquent compared with kids not in Head Start, against the alternative that those in Head Start are less likely to be arrested and sent to court as juveniles. Use an alpha of .05 in your hypothesis test and state each step in your hypothesis test. What is your interpretation about the value of Head Start?For your convenience, here is your data:

Head Start Not in Head Startn = 95 n = 125

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:



22. You have a problem on your police force of a group of 10 identified officers who have had an unusually high number of citizen complaints filed against them. Rather than fire these officers, you send them to a training session dealing with how to interact better with citizens. You have a record of the number of citizen complaints against each of these 10 officers in the year both before and after the training session. Test the null hypothesis that the training session had no effect on the number of citizen complaints against the alternative that the session reduced the number of complaints the officer had filed against them. Use an alpha of .01 in your hypothesis test and explicitly state each step. What is your conclusion about the training session?

Here is your data:

Officer Number of Number ofComplaints Before Complaints After

1 7 32 9 63 14 114 8 95 12 56 7 47 10 48 9 69 11 1010 16 15

Here’s a hint: The standard deviation of the difference scores is 2.357.

a. Calculate and interpret the average difference score.

b. Test the null hypothesis that the training session had no effect on the number of citizen complaints against the alternative that the session reduced the number of complaints the officer had filed against them. Use an alpha of .01 in your hypothesis test and explicitly state each step. What is your conclusion about the training session?

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:



23. Does getting married lead criminal offenders to quit crime (desist)? To test this you take a sample of 10 men who as juveniles spent time in a reform school, and a matched group of 10 men (matched no age, social class, and race) who also spent time in a juvenile reform school but did not get married. You collect data on the number of offenses they committed between 17 and 40 and here are your results for the two groups:

Mean NStd.

DeviationStd. Error

MeanPair 1 Married 4.4000 10 1.64655 .52068

Not Married

2.6000 10 1.50555 .47610

Other helpful information:

Test the null hypothesis that being married as an adult is unrelated to desistance or quitting crime against the alternative that those who get married as adults commit less crime between the ages 18 and 32 than those who stay single. Use an alpha of .05 and state each step of your hypothesis test. What do you conclude?

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

24. Do long prison sentences result in a lower crime rate? You divide 24 states where you have violent crime rate data into how severe their punishments are for violent felonies into three groups:

(1) Low severity (sentences on average for violent offenses are less than 5 years)(2) Medium severity (sentences on average for violent offenses are between 5 and 10 years)(3) High severity (sentences on average for violent offenses are more than 10 years)

Then, using the FBI’s Uniform Crime Reports, you get the violent crime rate for these 24 states.

Here are your data where each entry is the rate of violent crime in that state in 2014:



Low Severity Medium Severity High Severity

8.3 9.2 10.57.6 11.1 12.78.0 10.7 10.46.9 9.7 8.98.0 12.5 11.97.3 10.8 11.17.9 8.7 9.28.6 13.7 14.2

n1 = 8 n2 = 8 n3 = 8

Hint: Total sum of squares = 96.446

a. With this data, test the null hypothesis that µlow = µmedium = µhigh against the alternative that µlow = µmedium = µhigh, use an alpha of .01 and state each step of your hypothesis test. What do you conclude about sentence severity and violent crime rates?

Step 1:

Step 2:

Step 3:

Step 4:

ANOVACrime Rate

Sum of Squares df Mean Square F

Between GroupsWithin GroupsTotal 96.446

Step 5:



c. Using a critical difference score of |2.32|, which pair of means are different, and what would you conclude now about the relationship between sentence severity and violent crime rates?

d. Calculate and interpret the strength of the relationship between sentence length severity and the rate of violent crime.

25. You work in the research section of the Maryland Department of Probation and Parole and your department ran an experiment in which four different types of probation treatment were tried on its probation clients:

a. probation onlyb. probation and finec. probation and short jail termd. probation and long jail term

After a year, you collected information on the number of new arrests each person had during their year of probation. The mean number of mean arrests for each group are reported below.

Your boss comes to you and asks, “Based on the results of the experiment, which treatment should we use in the future and why.” You have to answer this question based on the data provided:

SSTotal = 335.10SSBetween = 125.70

a. What is your independent variable here and what is your dependent variable?

b. Conduct a hypothesis test that different probation treatments have no effect on the number of new arrests against the alternative that some treatment is better than some other. Use an alpha of .01.

Step 1:

Step 2:



Step 3:

Step 4:

Step 5:

c. Suppose your critical difference (CD) score was |3.58|, which pair of means are significantly different?

d. How much variation in new arrests are you explaining by knowing what treatment group someone was in?

e. What course of action will you tell your boss to take regarding the best probation treatment program and why?

26. You work in a police department that is being sued by the American Civil Liberties Union. They claim that there are significantly more complaints against the police in poor neighborhoods than the rich neighborhoods you serve. You look at all complaints made against police officers in your department for the last year and classify them as either being made by citizens in poor or more affluent neighborhoods. You then calculate the mean number of citizen complaints in each of the two neighborhoods. Here are your data:

Test the null hypothesis that the two population means are equal against the alternative that they are different from each other. Use an alpha of .01, with 23 df, and you cannot assume that the two population standard deviations are equal (σ1 ≠ σ2). State each step of your hypothesis. Will you win or lose the law suit? Explain.

Step 1:

Step 2:

Step 3:



Step 4:

Step 5:

27. You are interested in understanding the property crime rates in different neighborhoods in your state. You take a sample of 20 neighborhoods and collect information on three variables:

their property crime rate (y)whether the police use foot patrol (coded as “1”) or car patrol (coded as “0”) (x1)the divorce rate in the neighborhood (x2)

Here is your data:

Prop.Crime DivorceRate Patrol Rate

(y) (x1) (x2)23.40 .00 4.5044.00 .00 6.4036.70 .00 5.0043.00 .00 8.7018.00 .00 2.9045.00 .00 7.9038.60 .00 6.5044.20 .00 6.407.00 .00 1.7051.00 .00 9.2011.00 1.00 2.3013.20 1.00 9.2016.70 1.00 8.7019.50 1.00 3.0018.40 1.00 4.2021.00 1.00 7.9020.00 1.00 8.5014.40 1.00 4.3017.10 1.00 3.8011.00 1.00 2.50

And some supporting information:

ryx1 = -.69ryx2 = .55rx1x2 = -.096



a. You ran a bivariate regression with crime rate as the dependent variable and the type of neighborhood patrol practice as the independent variable, here are your results:

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t Sig.B Std. Error Beta1 (Constant) 35.090 3.274 10.717 .000

FootPatrol -18.860 4.630 -.693 -4.073 .001a. Dependent Variable: Property Crime Rate

Interpret the intercept, the slope coefficient, and whether your failed to reject or rejected the null hypothesis that βfootpatrol = 0 (with an alpha of .05). How much variance in property crime rates does type of police patrol explain?

b. You ran a bivariate regression with crime rate as the dependent variable and the neighborhood divorce rate as the independent variable, here are your results:

Coefficientsa

Model

Unstandardized Coefficients


t Sig.B Std. Error Beta1 (Constant) 8.744 6.694 1.306 .208

Divorce Rate

2.978 1.079 .545 2.760 .013

a. Dependent Variable: Property Crime Rate

Do a scattergram of the relationship between the divorce rate and crime. Interpret the intercept, the slope coefficient, and whether your failed to reject or rejected the null hypothesis that βdivorce rate = 0 (with an alpha of .05). How much variance in property crime rates does foot patrol explain?

c. You then ran a multivariate regression with neighborhood crime rates as the dependent variable and both type of police patrol and neighborhood divorce rate as the independent variables. Here’s what you got:

Coefficientsa

Model Unstandardized Coefficients


t Sig.



B Std. Error Beta1 (Constant) 19.470 4.925 3.954 .001

Divorce Rate

2.638 .716 .483 3.687 .002

Foot Patrol -17.594 3.568 -.646 -4.931 .000a. Dependent Variable: Property Crime Rate

R2 = .68

Interpret the intercept, the slope coefficient, and whether your failed to reject or rejected the null hypothesis that βdivorce rate = 0 and βfootpatrol = 0 (with an alpha of .05). Which variable has the stronger effect on property crime rates, and why do you say this? How much variance in property crime rates does foot patrol and divorce rates explain? Finally, was the neighborhood divorce rate a good second variable to add to your original regression equation that had only foot patrol in it? Why do you say this?

28. Here is a graph that shows the relationship between murder rates and the percentage of the population that has a handgun for 20 cities in the United States.

The correlation here is r = .21

Here is a second graph of the same data where we added only one new data point.



The correlation now is r = .47.

How do you explain this?

New Data Point

Documents

study.sagepub.com · Web viewWe take a random sample of 50 inmates currently convicted and incarcerated for aggravated assault, their sentence lengths are reported below. Stated Limits