The state and local police departments are trying to analyze

The state and local police departments are trying to analyze crime rates so they can shift their patrols from decreasing-rate areas to areas where rates are increasing. The city and county have been geographically segmented into areas containing 4,900 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 980 of the 4,900 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:

Solution

Answer:

P-bar = Mean crime / (number of months x sample size)

Here

mean crime = 10.167

number of months = 12

Sample size = 980

P-bar = 10.167/(12 x 980) = 0.000865

Therefore

S-p = square root of ( p-bar(1 – p bar)/ sample size)

S-p = square root of ( 0.000865(1 – 0.000865)/ 980) = 0.000939

UCL = p-bar + 1.96 s-p = 0.000865 + 0.001841 = 0.00271

LCL = p-bar - 1.96 s-p = 0.000865 - 0.001841 = -0.000976

The process is in control. Therefore, it can be stated that the crime rate has not increased. However, there appearsto be a gradual increase in the crime rate