Biology and Environmental Science

The indoor air quality (the concentration of particles less than 2.5 microns in diameter) in 15 bars, restaurants, and other public venues in Louisville was measured prior to the introduction of new smoking regulations. Two months after all public venues were required to be smoke-free, the air quality was measured again. The data (in μg/m3 ) are given in the following table.

Suppose the underlying before and after distributions of air quality are continuous.

a. Conduct a sign test with a = 0.05 to determine whether there is any evidence that the median amount of particulates decreased after the smoking regulations went into effect.

b. Conduct a Wilcoxon signed-rank test with a = 0.05 to determine whether there is any evidence that the median amount of particulates was greater before the smoking regulations went into effect than after.

c. Use the Wilcoxon rank-sum test with a = 0.05 to determine whether there is any evidence that the median amount of particulates decreased after the smoking regulations went into effect.

d. Compare the results of these three statistical tests. Which test(s) is(are) appropriate and why?