Question

2. For a sample of 900 police officers at a local police department, a researcher believes there is a relationship between “number of arrests per month” and “police use of force.” Using the following data, test the null hypothesis at the .01 level of significance that police use of force does not differ by the number of arrests per month that an officer makes. In so doing, identify: (1) the research and null hypothesis, (2) the critical value needed to reject the null, (3) the decision that you made upon analyzing the data, and (4) the conclusion you have drawn based on the decision you have made.

                                                                 Number Of Arrests Per Month

            Use of Force                           One                  Two                 Three               Four or More               Total

            No Force                                  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 and different from a t-test for two samples?

4. What statistical test would a researcher use to test the following research hypothesis: Individuals who report less favorable attitudes toward the police (measured as 1 = very favorable, 2 = somewhat favorable, 3 = somewhat not favorable, and 4 = not at all favorable) are more likely to be sentenced to higher security prisons (measured as 1 = minimum, 2 = medium, and 3 = maximum).

5. Why is it not possible to calculate a chi-square on the following hypothesis: Males have a higher number of total arrests than females?

6. Why is it impossible to calculate a negative F value when using an Analysis of Variance to test a hypothesis?

Answer 1

	Group 1	Group 2	Group 3	Group 4
	120	100	40	120
	120	140	100	160
	240	240	140	280
Sum =	480	480	280	560
Average =	160	160	93.333	186.667
\sum_i X_{ij}^2 =∑i​Xij2​=	86400	87200	31200	118400
St. Dev. =	69.282	72.111	50.332	83.267
SS =	9600	10400	5066.6666666667	13866.666666667
n =	3	3	3	3