Statistics in Criminal Justice

Multiple Choice (3 points each)

  1. Which of the following correlation coefficients signifies the weakest correlation?
    A. -0.28
    B. -0.76
    C. +0.12
    D. +0.66
  2. If fear of crime initially decreases with age, but then increases with age after age 40, the correlation between age and fear of crime would be _.
    A. Positive
    B. Negative
    C. Significant
    D. Curvilinear
  3. A null hypothesis in an ANOVA test will be rejected if __.
    A. Variance between groups is significantly larger than variance within groups
    B. Variance within groups is significantly larger than variance between groups
    C. The F-ratio is less than the critical F-value
    D. The observed frequencies are significantly different from the expected frequencies
  4. The shape of the t-distribution begins to more closely resemble the normal curve (z-distribution) as:
    A. Degrees of freedom decrease
    B. Degrees of freedom increase
    C. The obtained t-value increases
    D. The standard error of the difference between means decreases  
    Short Answer. Your answer must be at least 3 sentences long and written in complete sentences (5 points each).
  5. How is the logic of an ANOVA test similar to that of a t-test? Be sure to discuss how the equation for the obtained t-value is similar to the equation for the F-ratio.
  6. Why can’t we definitely conclude that two strongly correlated variables have a causal relationship? Use an example in your answer.
  7. Why do we convert sum of squares to mean squares when conducting an ANOVA?  
    For all questions involving calculations, you are required to show your work. If you don’t, I will take points off.
    For questions 8-12, use the following scenario.
    A researcher is interested in whether juvenile defendants who are released pending adjudication differ in terms of time to disposition compared to juveniles defendants who are detained. Released juveniles (N = 134) had a mean of 4.14 months to disposition (s = 3.77). Detained juveniles (N = 68) had a mean of 3.62 months to disposition (s = 4.25). Assuming equal population variances, conduct a t-test.
  8. State the null and research hypotheses. Write in full and complete sentences (4 points).
    Null:

Research:

  1. Calculate the standard error of the difference between means (4 points).
  2. Calculate the obtained t-value (5 points).
  3. Calculate the degrees of freedom and using a significance level of .01, obtain a critical t-value (3 points).
  4. Make a decision regarding the null hypothesis, explain how you came to this decision, and interpret your findings (5 points).

For questions 13-16, use the following scenario.
A researcher uses the JDCC (Juvenile Defendants in Criminal Courts) data to examine whether juvenile offenders charged with property crimes differ in terms of total number of charges compared to juvenile offenders charged with violent crimes. She conducts the t-test in SPSS and is willing to take a 5% risk of a false positive.

Independent Samples Test
Levene’s Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower Upper
Total number of charges Equal variances assumed 34.081 .000 4.761 1293 .000 1.498 .315 .881 2.116
Equal variances not assumed 7.041 1287.925 .000 1.498 .213 1.081 1.916

  1. State the null and research hypotheses. Write in full and complete sentences (4 points).
    Null:

Research:

  1. What are the results of Levene’s test? (Note: do not just say pass or fail/reject or fail to reject. Say what we can or cannot assume) (3 points).
  2. State the obtained t-value for the t-test (3 points).
  3. Make a decision regarding the null hypothesis, explain how you made your decision, and interpret your findings (5 points).

For questions 17-26, use the following scenario.
In a sample of juvenile offenders sent to boot camp, a juvenile probation officer is examining the relationship between number of prior police contacts before participating in the boot camp and number of offenses after participating in the boot camp. Calculate the correlation coefficient and conduct a hypothesis test to examine whether there is a significant relationship between number of prior police contacts and number of subsequent offenses.
Number of Prior Police Contacts (X) Number of Offenses (Y)
3 2
4 5
7 4
1 0
0 1
0 3
5 4
3 5

  1. State the null and research hypotheses. Write in full and complete sentences (4 points).
    Null:

Research:

  1. Calculate the correlation coefficient for the relationship between number of prior police contacts and number of offenses (5 points).
    Number of Prior Police Contacts (X) Number of Offenses (Y) XY x2 y2
    3 2
    4 5
    7 4
    1 0
    0 1
    0 3
    5 4
    3 5
    x = y = xy = x2 = y2 =
  2. State the strength and the direction of the relationship between number of prior police contacts and number of offenses (4 points).
  3. Calculate the coefficient of determination. What percentage of the variation in number of offenses can be explained by number of prior police contacts? (4 points).
  4. Calculate the obtained t-value (5 points).
  5. Calculate the degrees of freedom and using a significance level of .05, obtain a critical t-value (3 points).
  6. Make a decision regarding the null hypothesis, explain how you came to this decision, and interpret your findings (5 points).
  7. Regardless of the conclusion of the hypothesis test, the juvenile probation officer wishes to create a regression line and use the number of prior police contacts to predict the number of subsequent offenses. Calculate the slope coefficient for this regression line (5 points).
    Number of Prior Police Contacts (X) Number of Offenses (Y) XY x2
    3 2
    4 5
    7 4
    1 0
    0 1
    0 3
    5 4
    3 5
    x = y = xy = x2 =
  8. Calculate the y-intercept for the regression line (4 points).
  9. What is the predicted number of offenses for a boot camp participant who had 2 prior police contacts before being sent to the boot camp? (3 points).
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