Some citizens complained to city council members that there should be equal prot

Question

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence.

         The city has been broken down into 20 geographic areas, each containing 5,500 residences. The 1,100 sampled from each area showed the following incidence of crime during the past month:

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence.

         The city has been broken down into 20 geographic areas, each containing 5,500 residences. The 1,100 sampled from each area showed the following incidence of crime during the past month:

Explanation / Answer

P’=Total number of defects/Total number of samples

P’=Total number of defects/no of samples*sample size of each sample

P’=355/(1100*20)= 0.01614

Standard deviation Sp=(p’*(1-p’)/n)^0.5 where n=sample size=1100

Standard deviation=Sp=(0.01614*(1-0.01614)/1100)^0.5=0.00380

UCL=p’+z*Sp=0.01614+1.96*0.0038=0.023588

LCL=p’-z*Sp=0.01614-1.96*0.0038=0.008692

Number of samples for which Crime rate (p value) >UCL or p value <LCL=7

Area 2,6,10,16,17,19,20 (7 rows)

Thus Probability=7/20=0.35, which is outside 0.05 significance level(confidence interval 95%)

Thus Process is out of statistical control.

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