Question

GSU president is 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 5,100 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 1,020 of the 5,100 residences for data on crime. (Respondents are namelessness.) Here are the data collected for the past 12 months for one area:

MONTH          CRIME                        SAMPLE         CRIME

                    INCIDENCE          SIZE             RATE

January           9                      1,020            0

February         11                     1,020             0

March               9                       1,020            0

April                  9                        1,020            0

May                  9                        1,020            0

June                11                       1,020            0

July                 10                       1,020            0

August             12                       1,020            0

September      10                       1,020            0

October           13                       1,020            0

November       11                       1,020            0

December       10                       1,020            0

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.)

P−     

Sp       

UCL    

LCL    

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

January = 10 (out of 1,020 sampled)

February = 12 (out of 1,020 sampled)

March = 11 (out of 1,020 sampled)

What comments can you make regarding the crime rate?

            The process is in control.

            The process is out of control

Answer 1

a.

we first calculate p-bar i.e the center line

p-bar =AVERAGE(E3:E14)=0.01013

Next, we calculate Sp =sqrt(p-bar(1-p-bar)/n))

=sqrt(0.01013*(1-0.01013)/1020))

Sp=0.00314

UCLp =p-bar+z *Sp=0.01013+1.96*0.00314=0.01628

LCLp=p-bar-z*Sp=0.01013-1.96*0.00314=0.00399

Calculations are as shown below:

b.We calculate sample crime rate(p values ) for next three months as :

p value of January=10/1020=0.00980

p value of February=12/1020=0.01176

p value of March=11/1020=0.01078

All the p values lie within the control limits and hence the process is in control.