Final answer:
The appropriate hypotheses to test if the number of graffiti incidents declined are H0: μd ≥ 0 (no decrease in incidents) versus H1: μd < 0 (a reduction in incidents).
Step-by-step explanation:
To determine whether the number of graffiti incidents declined after the institution of a citizen Community Watch program, you would set up a hypothesis test. The null hypothesis (H0) typically states that there is no change, no effect, or no difference, and is tested against an alternative hypothesis (H1) that indicates the presence of an effect or difference. In this case, assuming μd is the mean difference in graffiti incidents before and after:
H0: μd ≥ 0 versus H1: μd < 0,
where the null hypothesis suggests that the mean difference is greater than or equal to zero, implying no reduction in incidents or an increase. The alternative hypothesis suggests that the mean difference is less than zero, which would imply a reduction in incidents. The appropriate choice is H0: μd ≥ 0 versus H1: μd < 0, as we are interested in testing if there has been a decrease in graffiti incidents.
Note that the listed hypotheses as 'a)' and 'b)' are inversely formulated relative to the conventional representation. The null hypothesis is typically represented as 'H0' while the alternative as 'H1'.