The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.1 mg, with a standard deviation of 3.2 mg. The mean tar content of a simple random sample of 25 filtered 100 mm cigarettes is 13.2 mg with a standard deviation of 3.7 mg.
Assume that the two samples are independent simple random samples, selected from normally distributed populations. Do not assume that the population standard deviations are equal, unless your instructor stipulates otherwise.
a. Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have a mean tar content greater than that of filtered 100 mm cigarettes.
b. What does the result suggest about the effectiveness of cigarette filters?