Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of \(124.32 \mu \mathrm{g} / 1\) and a SD of \(37.74 \mu \mathrm{g} / 1\); a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of \(35 \mu \mathrm{g} / 1.

(a) Write down the hypotheses that would be appropriate for testing if the police officers appear to have been exposed to a higher concentration of lead.

(b) Explicitly state and check all conditions necessary for inference on these data.

(c) Test the hypothesis that the downtown police officers have a higher lead exposure than the group in the previous study. Interpret your results in context.

(d) Based on your preceding result, without performing a calculation, would a \(99 \%\) confidence interval for the average blood concentration level of police officers contain \(35 \mu \mathrm{g} / 1\) ?

(e) Based on your preceding result, without performing a calculation, would a \(99 \%\) confidence interval for this difference contain 0 ? Explain why or why not.