Question

2. Generic drugs are lower-cost substitutes for brand-name drugs. Before a generic drug can be sold in the US, it must be tested and found to perform equivalently to the brand-name drug. The US Food and Drug Administration is supervising the testing of a new generic antifungal ointment. The brand-name ointment is known to deliver a mean of 3.5 micrograms of active ingredient to each square centimeter of skin. As part of the testing, seven subjects apply the ointment. Six hours later, the amount of active ingredient which has been absorbed into the skin is measured. The amounts in micrograms are: 2.6 3.2 2.1 3.0 3.1 2.9 3.7

Does the mean amount of generic drug absorbed differ from the mean amount absorbed by the brand-name drug? Use α = 0.01

Answer 1

= (2.6 + 3.2 + 2.1 + 3 + 3.1 + 2.9 + 3.7)/7 = 2.94

s = sqrt(((2.6 - 2.94)^2 + (3.2 - 2.94)^2 + (2.1 - 2.94)^2 + (3 - 2.94)^2 + (3.1 - 2.94)^2 + (2.9 - 2.94)^2 + (3.7 - 2.94)^2)/6) = 0.4995

The test statistic is

  

df = 7 - 1 = 6

At = 0.01, the critical values are +/- t0.005, 6 = +/- 3.708

Since the test statistic value is not ess than the Lower critical value, so we should not reject the null hypothesis.

At 0.01 significance level, there is not sufficient evidence to conclude that the mean amount of generic drug absorbed fdiffer fom the mean amount absorbed by the brand-name drug.