Question 360460: The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.
Number of Crimes by Area
A B C D E F G H
before 14 7 4 5 17 12 8 9
after 2 7 3 6 8 13 3 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! The following are the values for the before-minus-after values:
d = 12, 0, 1, -1, 9 , -1, 5 , 4
The average m of these values are 29/8 = 3.625.
Now the following corresponding values for  are
70.14,13.14,6.89,21.39,28.89,21.39,1.89,0.14.
Their sum is 163.87.
The standard deviation of the differences would be  , and the standard error is  .
Now we use a one-tailed matched-pairs t-test.
Null hypothesis: D = 0
Alternative hypothesis: D > 0
 , under assumption of the null hypothesis.
Now  , so the p-value is 0.0359. Since 0.0359>0.01, we don't reject the null hypothesis. Hence the differences in the sample aren't significant to say that there is a drop in the number of crimes.
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