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 5,000 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 800 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area: MONTH January February March April May June July August September October November December CRIME INCIDENCE 13 7 12 p bar Sp UCL LCL 8 13 7 8 12 10 14 10 8 SAMPLE SIZE 800 800 800 800 800 800 800 800 800 800 800 800 CRIME RATE 0.01625 0.00875 0.01500 0.01000 0.01625 0.00875 0.01000 0.01500 0.01250 0.01750 0.01250 0.01000 a. Determine the P, Sp, UCL and LCL for a p-chart of 95 percent confidence (at Z= 1.96). Note: Round your answers to 5 decimal places. b. If the next three months show crime incidences in this area as
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 5,000 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 800 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area: MONTH January February March April May June July August September October November December CRIME INCIDENCE 13 7 12 p bar Sp UCL LCL 8 13 7 8 12 10 14 10 8 SAMPLE SIZE 800 800 800 800 800 800 800 800 800 800 800 800 CRIME RATE 0.01625 0.00875 0.01500 0.01000 0.01625 0.00875 0.01000 0.01500 0.01250 0.01750 0.01250 0.01000 a. Determine the P, Sp, UCL and LCL for a p-chart of 95 percent confidence (at Z= 1.96). Note: Round your answers to 5 decimal places. b. If the next three months show crime incidences in this area as
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text: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 5,000 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 800 of the 5,000 residences for data on crime. (Respondents are
guaranteed anonymity.) Here are the data collected for the past 12 months for one area:
MONTH
January
February
March
April
May
June
July
August
September
October
November
December
p bar
CRIME
INCIDENCE
13
7
12
8
13
7
8
12
Sp
UCL
LCL
2498
10
14
10
SAMPLE SIZE
800
800
800
800
800
800
800
800
800
800
800
800
a. Determine the P, Sp, UCL and LCL for a p-chart of 95 percent confidence (at Z= 1.96).
Note: Round your answers to 5 decimal places.
CRIME RATE
0.01625
0.00875
0.01500
0.01000
0.01625
0.00875
0.01000
0.01500
0.01250
0.01750
0.01250
0.01000
b. If the next three months show crime incidences in this area as
January = 10 (out of 800 sampled)
February = 12 (out of 800 sampled)
March = 11 (out of 800 sampled)
What comments can you make regarding the crime rate?
O The process is in control.
O The process is out of control.
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