A local police precinct has seen a recent increase in the number of complaints filed regarding how officers are interacting with the public. Before addressing the issue, the commander wants to know if the issue is wide spread throughout the precinct or if it is isolated to the specific complainants. To determine this, the commander has the community relations unit randomly call houses throughout the precinct and ask how fairly they feel the police treats the public. The commander then compares the information gathered through the random sample to the known parameters for the entire city to determine if his precinct's score is significantly lower than average.
a) Would the commander conduct a 1-tailed or 2-tailed hypothesis test? Explain why.
b) Use the information below to conduct a z-test using p=.01 as your alpha level. Make sure you complete all 5 steps and show your work/answers for each step. (step 1:state hypothesis Step2:calculate standard error step 3:determine critical value step4:conduct hypothesis test step 5:make a decision about rejecting/failing to reject the hypothesis)
Sample; Mean = 2.64 SD=0.56 n=86
Population; Mean=2.72 SD=0.31
c) Calculate a 99% confidence interval for the above sample.