27 Treating cancer with yoga. According to a study funded by the National Institutes of Health, yoga classes can help cancer survivors sleep better. The study results were presented at the June 2010 American Society of Clinical Oncology’s annual meeting. Researchers randomly assigned 410 cancer patients (who had finished cancer therapy) to receive either their usual follow-up care or attend a 75-minute yoga class twice per week. After four weeks, the researchers measured the level of fatigue and sleepiness experienced by each cancer survivor. Those who took yoga were less fatigued than those who did not.

a. Assume the patients are numbered 1 through 410. Use the random number generator of a statistical software package to randomly assign each patient to either receive the usual follow-up care or to attend yoga classes.
Assign 205 patients to each treatment.

b. Consider the following treatment assignment scheme.
The patients are ranked according to severity of cancer and the most severe patients are assigned to the yoga class while the others are assigned to receive their usual follow-up care. Comment on the validity of the results obtained from such an assignment.