Question

Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 4 7 elgin corners 5 8 elm grove 2 1 greenburg 3 10 huntley 4 6 north lyman 8 8 south lyman 2 6 pin oak 5 5 victorville 5 9 pictureclick 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.
a. h1: μd ≤ 0 versus h0: μd > 0.
b. h0: μd ≥ 0 versus h1: μd < 0. a b

Answer 1

The data are reported in the attached table.

We define the null hypothesis H₀ as the statement that is believed true until we prove it wrong with the test.
We define the alternative hypothesis H₁ as the statement we want to conclude with our test.

The difference in graffiti before (B) and after (A) will be:
d = A - B.

If the graffiti declined, it means that A will be smaller than B, therefore d should be negative.

Therefore we can set:
H₀ : μd  ≥ 0
H₁ : μd < 0 

The equal sign would mean that the number of graffiti incidents remained constant, therefore it is part of the null hypothesis.

Therefore the correct answer is B) H₀: μd ≥ 0 versus H₁: μd < 0