The state and local police departments are trying to analyze crime rates so they
ID: 353819 • Letter: T
Question
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 5,600 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 1,120 of the 5,600 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:
b. If the next three months show crime incidences in this area as
January = 10 (out of 1,120 sampled)
February = 12 (out of 1,120 sampled)
March = 11 (out of 1,120 sampled)
What comments can you make regarding the crime rate?
MONTH CRIME INCIDENCE SAMPLE SIZE CRIME RATE January 9 1,120 0 February 11 1,120 0 March 9 1,120 0 April 9 1,120 0 May 9 1,120 0 June 11 1,120 0 July 9 1,120 0 August 12 1,120 0 September 10 1,120 0 October 13 1,120 0 November 13 1,120 0 December 10 1,120 0
Explanation / Answer
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 5,600 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 1,120 of the 5,600 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:
MONTH
CRIME INCIDENCE
SAMPLE SIZE
CRIME RATE
January
9
1,120
0
February
11
1,120
0
March
9
1,120
0
April
9
1,120
0
May
9
1,120
0
June
11
1,120
0
July
9
1,120
0
August
12
1,120
0
September
10
1,120
0
October
13
1,120
0
November
13
1,120
0
December
10
1,120
0
1. Determining the = Total number of defective units from all samples (Crime Incidence)
Number of samples X sample size
= 125/ 12X 1120
=125/ 13440
= .009
2. Determining the
= Putting values of
= [.009(1-.009)/ 1120]1/2
Sp= .003
3. Determine the UCL=
= .009+ 1.96(.003)
UCL = .015
4. Determine the LCL=
= .009 - 1.96(.003)
LCL =.003
MONTH
CRIME INCIDENCE
SAMPLE SIZE
CRIME RATE
January
9
1,120
0
February
11
1,120
0
March
9
1,120
0
April
9
1,120
0
May
9
1,120
0
June
11
1,120
0
July
9
1,120
0
August
12
1,120
0
September
10
1,120
0
October
13
1,120
0
November
13
1,120
0
December
10
1,120
0
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