In experiments to determine the effectiveness of drugs such

In experiments to determine the effectiveness of drugs such as anti-fungal ointments that are applied to the skin, the concentration of the drug in a patient\'s skin must be measured. A particular article describes an improved method of measuring that is designed to assure that all the drug in the skin is recovered. Assume that in an experiment using the old method, the mean amount of the drug recovered from a sample of 47 patients was 105 ng with a standard deviation of 20 ng, and that in an experiment using the new method the mean amount of drug recovered in a sample of 34 patients was 116 ng with a standard deviation of 15 ng. Find a 98% confidence interval for the difference in the mean amounts recovered between the two methods. Round your final answers to three decimal places. The confidence interval is

Solution

Given a=0.02, Z(0.01) = 2.33 (from standard normal table)

So 98% confidence interval is

(xbar1-xbar2) +/- Z*sqrt(s1^2/n1+s2^2/n2)

--> (105-118) +/- 2.33*sqrt(20^2/48+15^2/35)

--> (-21.952, -4.048)