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 5,050 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 1,010 of the 5,050 residences for data on crime. (Respondents are guaranteed anonymity.) The 1,010 sampled from each area showed the following incidence of crime during the past month:

AREA	NUMBER OF CRIMES	SAMPLE SIZE	CRIME RATE
1	13	1,010	0.013
2	2	1,010	0.002
3	18	1,010	0.018
4	17	1,010	0.017
5	13	1,010	0.013
6	26	1,010	0.026
7	11	1,010	0.011
8	19	1,010	0.019
9	11	1,010	0.011
10	3	1,010	0.003
11	18	1,010	0.018
12	14	1,010	0.014
13	11	1,010	0.011
14	13	1,010	0.013
15	9	1,010	0.009
16	27	1,010	0.027
17	4	1,010	0.004
18	18	1,010	0.018
19	6	1,010	0.006
20	27	1,010	0.027
	280

a. Determine P−

, S_p, UCL and LCL for a p chart of 95 percent confidence (at Z = 1.96). (Round your answers to 4 decimal places.)

P−

Sp
UCL
LCL

b. What can you say about the process?

	Process is in statistical control.
	Process is out of statistical control.

Answer 1

a:

total	280	20200
steps and formulas, for z=		1.96
Proportion of defects=P	total nonconformities/total observations	0.0139
Q=	1-P	0.9861
N=	average sample size	1010
Standard deviation, Sp	squareroot(P*Q/N)	0.0037
UCL=	P + z*Sp	0.0211
LCL=	P - z*Sp	0.0067

b: No, the process is not in control. As we can see that proportions have gone above UCL.

Sample	defectives	observation	proportion= defectives/observations	UCL	LCL	P
1	13	1010	0.013	0.021	0.007	0.014
2	2	1010	0.002	0.021	0.007	0.014
3	18	1010	0.018	0.021	0.007	0.014
4	17	1010	0.017	0.021	0.007	0.014
5	13	1010	0.013	0.021	0.007	0.014
6	26	1010	0.026	0.021	0.007	0.014
7	11	1010	0.011	0.021	0.007	0.014
8	19	1010	0.019	0.021	0.007	0.014
9	11	1010	0.011	0.021	0.007	0.014
10	3	1010	0.003	0.021	0.007	0.014
11	18	1010	0.018	0.021	0.007	0.014
12	14	1010	0.014	0.021	0.007	0.014
13	11	1010	0.011	0.021	0.007	0.014
14	13	1010	0.013	0.021	0.007	0.014
15	9	1010	0.009	0.021	0.007	0.014
16	27	1010	0.027	0.021	0.007	0.014
17	4	1010	0.004	0.021	0.007	0.014
18	18	1010	0.018	0.021	0.007	0.014
19	6	1010	0.006	0.021	0.007	0.014
20	27	1010	0.027	0.021	0.007	0.014