An epidemiologist is trying to discover the cause of a certain kind of cancer. H

Question

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, exercise, and so on. His object is to determine for each factor if there is a difference between the mean value of the factor among those who develop cancer and among those who do not: a difference in means will suggest a connnection between the factor and the cancer. He will test the null hypothesis H0 : µ1 µ2 = 0 against H1 : µ1 µ2 6= 0 for each of the 48 factors (48 hypothesis tests in total). In an effort to be cautiously conservative, he uses a significance level of = 0.01 in all his tests. What is the probability that at least one of the factors will be found to be associated with the cancer, even if none of them is actually connected (that is, what is the probability of making at least one type I error)?

Explanation / Answer

Probability of type one error= 0.05, so probability if having no type one error in one test = 1-0.05 =0.95 , So probability of making no type one error in all of tests = power(0.95,48) = 0.0853 (as all tests are independent)

So probability of making at least one type I error = 1- Probability of making no type one error = 1-0.0853 = 0.9147 (ans)

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