Question

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

Answer 1

(1)

HA: Research Hypothesis: There is a relationship between “number of arrests per month” and “police use of force.”

H0: Null Hypothesis: There is no relationship between “number of arrests per month” and “police use of force.”

(2)

ndf = (r - 1) X (c - 1)

= (2 - 1) X (4 - 1)

= 3

= 0.01

From Table, critical value of = 11.3449

(3)

Observed Frequencies:

	One	Two	Three	Four or more	Total
No force	120	100	40	120	380
Force	120	140	100	160	520
Total	240	240	140	280	900

Expected Frequencies are calculated as follows:

Expected Frequencies:

	One	Two	Three	Four or more	Total
No force	240X380/900=101.33	240X380/900=101.33	140X380/900=59.11	280X380/900=118.22	380
Force	240X520/900=138.67	240X520/900=138.67	140X520/900=80.89	280X520/900=161.78	520
Total	240	240	140	280	900

Test Statistic is calculated as follows:

Observed (O)	Expected (E)	(O - E)2/E
120	101.33	3.44
100	101.33	0.02
40	59.11	6.18
120	118.22	0.03
120	138.67	2.51
140	138.67	0.01
100	80.89	4.52
160	161.78	0.02
Total =		16.72

Test Statistic = 16.72

Since calculated value of = 16.72 is greater than critical value of = 11.3449, the difference is significant. Reject null hypothesis.

(4)

Conclusion:

The data support the claim that there is a relationship between “number of arrests per month” and “police use of force.”