Question: 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.