An epidemiologist is trying to discover the cause of a certain kind of cancer. He studies a group of 10,000 people for five years, measuring 48 different “factors” involving eating habits, drinking habits, smoking, exercise, and so on. His object is to determine if there are any differences in the means of these factors (variables) between those who developed the given cancer and those who did not. He assumes that these variables are independent, even though there may be evidence to the contrary. In an effort to be cautiously conservative, he uses the 0.01 level of significance in all his statistical tests.
(a) What is the probability that one of these factors will be “associated with” the cancer, even if none of them is a causative factor?
(b) What is the probability that more than one of these factors will be associated with the cancer, even if none of them is a causative factor?