Brands of lacrosse helmets were compared for severity from front and back impacts. Impacts were measured with the Gadd Severity Index (where higher scores imply more severe impacts). A reduced dataset provides three replicates for each of four brands and impact locations. Location Brand Front Back 1033.12 894.646 1348.208 902.892 1071.822 1010.01 2 1077.465 1113.792 1067.588 1087.07 881.427 1188.106 3 613.375 1526.328 1144.626 1551.818 1013.652 1572.681 4 1387.522 1710.564 1332.813 1543.174 1142.812 1652.74 The hypotheses of interest are: 1. Ho : 71 = T2 = T3 = t4 (no main effect of the brand factor); H1: at least one t; + 0 2. Ho : B1 = B, (no main effect of the location factor); H1: at least one ; + 0 3. Ho : (Tf)11 = (TB)21 = ... = (Tf)42 (no interaction); H: at least one (t)j #0 (a) Test the hypotheses using the analysis of variance with a = 0.05. What are your conclusions? Round your answers to two decimal places (e.g. 98.76). 1. fo = fo.05.3. 16 = i i fo foos,3, 16 v Ho 2. fo = fo.05, 1, 16 i i fo fo.os, 1, 16 V Ho 3. fo = fo.05,3, 16 i i fo v fo.05,3,16 V Ho (b) Analyze the residuals from this experiment. The normal plot of the residuals indicates that the assumption of normality reasonable. (c) Using Fisher's LSD method, investigate the differences between the mean impact severity for the four brands. Use a = 0.05. Suppose that the interaction is negligible. Round your answer to one decimal place (e.g. 98.7). LSD = i The differences between Brands V are significant (at a = 0.05).