41. Are there drugs that will help a chronic insomniac get a good night s sleep? This problem was studied a hundred years ago ( The Action of Optical Isomers, II: Hyoscines, J. Physiol., 1905: 501—510).

Ten patients with chronic sleep loss were each tested on four treatments, of which one was no drug.

Here are the average hours of sleep for each patient with no drug and the average amount of sleep with the three drugs:

Patient 1 2 3 4 5 No drug 0.6 1.1 2.5 2.8 2.9 Drug 1.97 4.20 7.47 4.1 5.87 Patient 6 7 8 9 10 No drug 3.0 3.2 4.7 5.5 6.2 Drug 3.2 7.5 5 4.9 6.3

a. Verify graphically that the relevant normal distribution assumption appears appropriate.

b. Obtain a con dence interval for the population mean difference. Interpret your result in terms of the advantage or disadvantage of the drugs.