Suppose that we are testing whether five population means are equal to each other. We would normally use ANOVA for that, but suppose that we carry out separate hypothesis tests in which we compare the five means to each other, two at a time. Using a level of significance of 0.01, what is the probability of a Type I error in one or more of the pair-wise hypothesis tests?
a. 0.01 b. 0.05 c. 0.096 d. 0.99