Question: A team of researchers has developed a test that attempts to predict the use of the excessive force that police officers use against suspects. A series of observations on police recruits, psychological profiles, and scores from their police academy training are used to determine a “proneness to use excessive force” score. Ten years later, additional observations, profiles, and data from actual experience are gathered for the same officers that reflects the frequency and extent of excessive force repeatedly used. This score is called “force”. Suppose these procedures are used within a group of 10 officers who trained at “Academy A” and a separate group of 10 officers who trained at “Academy B.” Given the data provided, answer the questions below. (Use a=.05 and ignore the small N used to make computations easier- act as if N>20in each group except for df.) In formulating your answer to each question, list the hypotheses, assumptions, decision rules (including the critical values, directionality of the test, and degrees of freedom if appropriate), computation, and decision.

(a) Test the hypothesis that the officers sampled from Academy A and Academy B do not differ in their proneness to use excessive force score; in their force score.

(b) Suppose the data came from 10 police officer partners (Officer A from Academy A is he partner of Officer K from Academy B’s, etc.). Again test the hypothesis that officers from Academy A and officers from Academy B do not differ in their proneness to use excess force scores; in their force scores.

(c) Twice you have tested the hypothesis that officers from Academy A and officers from Academy B do not differ with respect to their proneness to use excessive force scores, once using an independent-groups test (c) and once using a correlated-groups test (b). Suppose, as is quite possible, the correlated groups analysis gave a significant result (H₀ rejected)but the independent-group analysis did not (H₀ not rejected0. Explain how this would be possible, and explain what advantage correlated groups research designs might have over independent-groups designs (if one has a choice).

(d) Test the hypothesis that there is no relationship between proneness to use excessive force score and the force score for officers trained at Academy A.

(e) Test the hypothesis that there is no relationship between the proneness to use excessive forces score and the force score for officers trained at Academy B.