The state and local police departments are trying to analyze crime rates so they

Question

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 6,000 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 1,200 of the 6,000 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:

a. Determine the PP , Sp, UCL and LCL for a p-chart of 95 percent confidence (at Z = 1.96). (Round your answers to 5 decimal places.)

b. If the next three months show crime incidences in this area as

January = 10 (out of 1,200 sampled)

February = 12 (out of 1,200 sampled)

March = 11 (out of 1,200 sampled)

What comments can you make regarding the crime rate?

The process is in control.

The process is out of control.

MONTH CRIME INCIDENCE SAMPLE SIZE CRIME RATE January 7 1,200 0 February 9 1,200 0 March 7 1,200 0 April 7 1,200 0 May 7 1,200 0 June 9 1,200 0 July 7 1,200 0 August 10 1,200 0 September 7 1,200 0 October 11 1,200 0 November 12 1,200 0 December 9 1,200 0

Explanation / Answer

a. Avg incidents of crime

Pbar = sum of all incidents / 12 x 1/1200

= 102/12 x1/1200 =0.007

UCL = Pbar + 3 [ Pbar (1-Pbar)/1200]1/2

= 0.007+ 3 (0.0024) = 0.00142

LCL will be zero because it is always desirable to have zero crime incidents.

Upper value of crime incidents according to limit

= 0.00142x1200 = 17.04

b. The process is under control because the incidents are within limits.

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