Knowing that yij - y = (yij - yi) + (yi - y) prove the following identity for a one-way ANOVA k ni k ni k E Z(y - y)? = EE(vis - 12)2 + Eni(yi -y)? i=1 j=1 i=1 j=1 i=1 Corrosion rates (percent) after application of a protective coating from 3 different sup- pliers were measured for machinery involved in chemical manufacturing using corrosize solvents. Do the following data indicate that the protective coatings differ for o=0.01? Supplier 1 14 13 9 15 11 13 14 11 Supplier 2 10 12 9 7 11 8 12 9 10 13 9 10 Supplier 3 11 5 9 10 6 8 8 7 The following are number of defects over 5 successive days of manufacturing for 4 different machines for a photolithography process. Test at the level of significance o=0.01 whether the differences among the 4 means can be attributed to chance. Machine 1 Machine 2 Machine 3 Machine 4 6 14 10 9 14 9 12 12 10 12 7 8 8 10 15 10 11 14 11 11