1. Based on her own experiences in court, a prosecutor believesthat some judges provide more severe punishments than other judgesfor people convicted of domestic violence. Five of the most recentdomestic violence sentences (in years) handed down by three judgesare recorded below.
Judge 1 | Judge 2 | Judge 3 |
1 | 3 | 1 |
1 | 2 | 5 |
3 | 4 | 2 |
2 | 3 | 1 |
2 | 4 | 1 |
Using this information, test the null hypothesis at the .05level of significance that judges do not vary in the sentencelengths imposed on individuals convicted of domestic violence. Inso doing, please: (1) identify the research and null hypotheses,(2) the critical value needed to reject the null, (3) the decisionthat you made upon analyzing the data, and (4) the conclusion youhave drawn based on the decision you have made.
2. For a sample of 900 police officers at a local policedepartment, a researcher believes there is a relationship between“number of arrests per month†and “police use of force.†Using thefollowing data, test the null hypothesis at the .01 level ofsignificance that police use of force does not differ by the numberof arrests per month that an officer makes. In so doing, identify:(1) the research and null hypothesis, (2) the critical value neededto reject the null, (3) the decision that you made upon analyzingthe data, and (4) the conclusion you have drawn based on thedecision you have made.
                                                               Number Of Arrests PerMonth
           Use of Force                         One                 Two                Three              Four orMore              Total
           NoForce                                 120                 100                40                     120                                 380
           Force                                     120                 140                100                     160                                  520_
                                                           240                 240                140                     280                                 900
3. How is an Analysis of Variance (ANOVA) similar to anddifferent from a t-test for two samples?
4. What statistical test would a researcher use to test thefollowing research hypothesis: Individuals who report lessfavorable attitudes toward the police (measured as 1 = veryfavorable, 2 = somewhat favorable, 3 = somewhat not favorable, and4 = not at all favorable) are more likely to be sentenced to highersecurity prisons (measured as 1 = minimum, 2 = medium, and 3 =maximum).
5. Why is it not possible to calculate a chi-square on thefollowing hypothesis: Males have a higher number of totalarrests than females?
6. Why is it impossible to calculate a negative F value whenusing an Analysis of Variance to test a hypothesis?
