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 5,200 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 1,040 of the 5,200 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area CRIME INCIDENCE MONTH SAMPLE SIZE CRIME RATE January June August September 8 a. Determine the P, Sp. UCL and LCL for a p-chart of 95 percent confidence (at Z-1.96).(Round your answers to 5 decimal places.)

Explanation / Answer

Total number of Defects (crime incidences) = 7+9+7+7+7+9+8+10+8+11+11+8 = 102

Total number of Observations = No. of samples*Sample Size = 12*920 = 11040

p bar = Total number of Defects / Total number of Observations

= 102 / 11040

= 0.009239

= 0.00924

Sp = Square root of { [ p bar ( 1 - p bar) ] / n }

= Square root of { [0.00924 ( 1 - 0.00924) ] / 920 }

= 0.00315

UCL = p bar + z*Sp

= 0.00924 + 1.96*0.00315

= 0.00924 + 0.00617

= 0.01541

LCL = p bar - z*Sp

= 0.00924 - 1.96*0.00315

= 0.00924 - 0.00617

= 0.00307

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