As part of your work for an environmental awareness group, you want to test a claim that the mean amount of lead in the air in U.S. cities is less than 0.036 microgram per cubic meter. You find that the mean amount of lead in the air for a random sample of 56 U.S. cities is 0.039 microgram per cubic meter and the standard deviation is 0.069 microgram per cubic meter. At α = 0.01, can you support the claim?

(a) Identify the claim and state H₀ and H_a, 

(b) Find the critical value(s) and identify the rejection region(s), 

(c) Find the standardized test statistic t, 

(d) Decide whether to reject or fail to reject the null hypothesis, and 

(e) Interpret the decision in the context of the original claim. Assume the population is normally distributed.