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 lower 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 60,000 residences. The 1,000 sampled from each area showed the following incidence of crime during the past month:

Area	Number of Crimes	Sample Size
1	14	1000
2	3	1000
3	19	1000
4	18	1000
5	14	1000
6	28	1000
7	10	1000
8	18	1000
9	12	1000
10	3	1000
11	20	1000
12	15	1000
13	12	1000
14	14	1000
15	10	1000
16	30	1000
17	4	1000
18	20	1000
19	6	1000
20	30	1000

1. Develop the appropriate control chart for the data above. Be sure to label the chart completely and accurately. Use a 99% confidence level.

2. Based on the control chart in (a), suggest a reallocation of crime protection effort for this city.

Answer 1

Answer a:

Based on the data provided, the most appropriate control chart that should be prepared is “p-chart”.

Area	Number of Crimes	Sample Size	p = Number of crimes/Sample Size
1	14	1000	0.014
2	3	1000	0.003
3	19	1000	0.019
4	18	1000	0.018
5	14	1000	0.014
6	28	1000	0.028
7	10	1000	0.010
8	18	1000	0.018
9	12	1000	0.012
10	3	1000	0.003
11	20	1000	0.020
12	15	1000	0.015
13	12	1000	0.012
14	14	1000	0.014
15	10	1000	0.010
16	30	1000	0.030
17	4	1000	0.004
18	20	1000	0.020
19	6	1000	0.006
20	30	1000	0.030
Average of all 20 observations (p bar)	0.015

p =          proportion of the defects in the sample               

p bar = mean or average of the proportions      

Sample size (n) = 1000  

p bar = Center Line (CL) = 0.0150              

z = no. of standard deviation from process average = 2.58 (for 99% confidence level)

Standard Deviation (σ) = √[p bar * (1- p bar)]/n                

σ = 0.0038438

                                                               

UCL= p bar+zσ = 0.0249

LCL= max(0,(p bar-zσ)) = 0.0051

Populate the data:

Plot the p-chart:

reallocation of crime protection effort for this city.

Answer (part 2):

The areas 2, 10 and 17 have crime which is less than the LCL which means that the crime rate is significantly less in these areas, so the police force and its efforts can be reduced and few force members can be moved to other critical areas. Area 19 is close to LCL so it can be relaxed to a certain extent.

Areas 6, 16 and 20 have their values breaching the UCL, indicating the level of crime is significantly high in these areas an extra police force should be mobilized from less critical areas (2, 10, 17 and 19) so that the effort can be done in controlling the crime situation in these areas.