The city of Metropolis is interested in using data to support decision-making, and have identified several issues and analyses below.
(a) Citizens have complained to city council members that there should be equal protection under the law against occurrence of crimes, such that high-crime areas should have more police protection than low-crime areas (e.g., increased police patrols, better street lighting). The city has been broken into 20 geographic areas, each containing 5,000 residences. In the past month, the police contacted a random sample of 1,000 residences in each area to ask about crime (the police recognize that not all crime is reported, and respondents were guaranteed anonymity), and recorded the number of crimes in each area is shown in Table 1.
Construct a p-chart, based on 3 sigma limits. What do you conclude? What would you suggest as next steps?
Table 1: Data for Problem 3
|
Area
|
# of Crimes
|
Area
|
# of Crimes
|
|
1
|
14
|
11
|
20
|
|
2
|
3
|
12
|
15
|
|
3
|
19
|
13
|
12
|
|
4
|
18
|
14
|
14
|
|
5
|
14
|
15
|
10
|
|
6
|
28
|
16
|
30
|
|
7
|
10
|
17
|
4
|
|
8
|
18
|
18
|
20
|
|
9
|
12
|
19
|
6
|
|
10
|
3
|
20
|
30
|
(b) Suppose that Metropolis received a grant that allowed them to improve street lighting, clear abandoned buildings, and implement other measures that have been shown to reduce the incidence of crime. They are interested in determining whether these measures have had an effect on the crime rate. The police contacted random sample of 1,000 residences in each of the city's 20 areas to ask about crime, for 6 months before the changes and for six months after. They recorded the number of crimes in each area as shown in Table 2 on next page.
Set up and carry out a hypothesis test (in Excel or another statistical package) to examine whether or not the number of crimes has been reduced. Clearly state the hypothesis that you are testing, and your conclusion. Use a Type I error tolerance of 5 percent.
Table 2: Number of Crimes in Each Area for Problem 3
|
Area
|
Average # of Crimes
Before Grant
|
Average # of Crimes After Grant
|
|
1
|
12.1
|
11
|
|
2
|
2.4
|
1.6
|
|
3
|
18.7
|
17
|
|
4
|
17
|
16.8
|
|
5
|
13.6
|
11
|
|
6
|
24.5
|
26.2
|
|
7
|
9.8
|
9
|
|
8
|
16.2
|
14.1
|
|
9
|
12.8
|
8.4
|
|
10
|
3.5
|
6
|
|
11
|
18
|
14.5
|
|
12
|
16.2
|
17
|
|
13
|
9.1
|
7.2
|
|
14
|
15.4
|
11.7
|
|
15
|
11.1
|
8.6
|
|
16
|
26.2
|
27.1
|
|
17
|
4.8
|
3.2
|
|
18
|
16.3
|
15.4
|
|
19
|
6.1
|
8
|
|
20
|
25
|
22.4
|