A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the
population standard deviation is 10.8 milligrams. At α = 0.01, can you reject the research organization’s claim?

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

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

(c) Find the standardized test statistic z, 

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

(e) Interpret the decision in the context of the original claim.