Question

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?

Answer 1

µd = µ_after - µ_before.

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