Question

As an engineer working for Thomson Pharmaceutical, you are in charge of developing a new cancer drug. The new drug is to be used as a supplement to a well established, currently used drug to reduce tumor sizes in lung cancer patients. Previous studies have shown that the currently-used drug results in an average reduction in tumor mass of 38.7% after 8 weeks of use. To study the effects of the new supplement, you had 16 patients who were given both the current drug and the new supplement drug simultaneously. These patents showed an average 44.7% reduction in tumor mass after 8 weeks (5.92% standard deviation). You also had another 16 patients who were given the current drug along with a placebo (sugar pill) that they thought was the new supplemental drug. This last group showed an average 39.8% reduction after 8 weeks (5.15% standard deviation). In order for development of the new drug to continue, you need to be 99% confident that the supplemental drug is better than the placebo. Determine whether this is true. (Assume the variances are equal for all the studies).

(a) Write the appropriate null, and alternative hypotheses.

(b) Determine the correct pooled statistic (S_p).

(c) Identify the critical region (i.e, the test statistic needs to satisfy what inequality in order to reject the null hypothesis?)

(d) Estimate the p-value for this test. Based on your analysis, can the development of the new drug proceed?

Answer 1