Statement of a problem № m40006


A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim. During your tests, you find that a random sample of twenty 12-ounce bottles of cola has a mean caffeine content of 39.2 milligrams. Assume the population is normally distributed and the population standard deviation is 7.5 milligrams. At α = 0.01, can you reject the company’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, (e) Interpret the decision in the context of the original claim. If convenient, use technology.

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