The pesticide diazinon is in common use to treat infestations of the German cockroach, Blattella germanica. A study investigated the persistence of this pesticide on various types of surfaces. Researchers applied a 0.5% emulsion of diazinon to glass and plasterboard. After 14 days, they randomly assigned 72 cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48 hours. On glass, 10 cockroaches died, while on plasterboard, 31 died.

(a) Construct and interpret a 95% confidence interval for the difference in the proportion of cockroaches that die on each surface. Assume all conditions have been met.

PG = True proportion of cockroaches that would die on treated glass. PP = True proportion of cockroaches that would die on plasterboard.