In: Statistics and Probability
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?
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