Five independent samples of 50 scores each are randomly drawn from popu¬lations that are normally distributed with equal variances. We wish to test the claim that μ1 = μ2 = μ3 = μ4 = μ5
a. If we used only the methods given in Chapter 8, we would test the individual claims μ1 = μ2 = μ3,........ ,. μ4How many ways could we pair off 5 means?
b. Assume that for each test of equality between two means, there is a 0.95 probability of not making a type I error. If all possible pairs of means are tested for equality, what is the probability of making no type I errors? (Although the tests are not actually independent, assume that they are.)
c. If we use analysis of variance to test the claim that μ1 = μ2 = μ3= μ4 = μ5 at the 0.05 level of significance, what is the probability of not making a type I error?
d. Compare the results of parts (b) and (c). Which approach is better in the sense of giving us a greater chance of not making a type I error?