Question

Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.

Answer 1

This is a problem on hypothesis testing on the difference of two dependent means. To solve for this one, the difference for each pair should be solved. 

After it, the mean and standard deviation of the differences should also be calculated.  Then, we state the null and alternative hypotheses. 

The null hypothesis is  $H_{0}: \mu_d=0$
The alternative hypothesis is  $H_a: \mu_d\ \textgreater \ 0$

These are the required hypotheses to see whether the number of graffiti incidents declined. 

Answer 2

In order to be clear, the data are reported in the picture attached.

The null hypothesis H₀ represents what is believed true if the data don't prove the opposite.
The alternative hypothesis H₁ is the conclusion we want to deduce from the test.

If we call d the difference in graffiti before (B) and after (A) (pay attention to the order) d = B - A.
We want to prove that the incidents are declined, therefore B should be greater than A and d would be positive.

Therefore:
H₀ : μd ≤ 0
H₁ : μd > 0