Question: A more efficient experiment than the one described in problem was carried out to determine whether a sleeping pill was effective. Each person in a random sample of 30 people was given the three treatments: drug, placebo, nothing. The order in which these treatments were administered was randomly chosen for each person in the sample.

a. Explain why this experiment is more efficient than the one described for the same investigation in problem 9-62. What is the name of the experimental design used here? Are there any limitations to the present method of analysis?

b. The results of the analysis include SSTR = 44,572, SSBL = 38,890, and SSE = 112,672. Carry out the analysis, and state your conclusions. Use α = 0.05.

Problem: Analysis of variance has long been used in providing evidence of the effectiveness of pharmaceutical drugs. Such evidence is required before the Food and Drug Administration (FDA) will allow a drug to be marketed. In a recent test of the effectiveness of a new sleeping pill, three groups of 25 patients each were given the following treatments. The first group was given the drug, the second group was given a placebo, and the third group was given no treatment at all. The number of minutes it took each person to fall asleep was recorded. The results are as follows.

Use a computer (or hand calculations) to determine whether the drug is effective. What about the placebo? Give differences in average effectiveness, if any exist.