Question

In: Statistics and Probability

Concerned about graffiti, mayors from 6 suburban communities instituted a citizen community watch program. To evaluate...

Concerned about graffiti, mayors from 6 suburban communities instituted a citizen community watch program. To evaluate the program, the number of graffiti incidents was recorded for the 2-month period before and after the program. Below are the results.

Community Incidents after Incidents before
Burr Oak 8 12
Elm Grove 7 8
North Lyman 0 5
South Lyman 4 4
Pin Oak 4 3
Victorville 0 3

At the 0.025 significance level, can it be concluded that the average number of graffiti incidents declined?

Solutions

Expert Solution

µd = µafter - µbefore.

Ho :   µd=   0
Ha :   µd <   0

Sample #1 Sample #2 difference , Di =sample1-sample2 (Di - Dbar)²
8 12 -4 4.00
7 8 -1 1.00
0 5 -5 9.00
4 4 0 4.00
4 3 1 9.00
0 3 -3 1.00
sample 1 sample 2 Di (Di - Dbar)²
sum = 23 35 -12 28.000

mean of difference ,    D̅ =ΣDi / n =   -2.000
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.3664

Level of Significance ,    α =    0.025                  
                          
sample size ,    n =    6                  
                          


std error , SE = Sd / √n =    2.3664   / √   6   =   0.9661      
                          
t-statistic = (D̅ - µd)/SE = (   -2 -   0   ) /    0.9661   =   -2.0702


                          
Degree of freedom, DF=   n - 1 =    5                  

  
p-value =        0.0466   [excel function: =t.dist(t-stat,df) ]              
Conclusion:     p-value>α , Do not reject null hypothesis                      
there is not enough evidence to conclude that average number of graffiti incidents declined at α=0.025


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