he quality of work performed was measured by an index taking into account veral characteristics of quality. Four agencies were chosen for each factor level m bination and the quality of their work evaluated. The data on quality are ailable at the website with allofthe datasetsfor the Kutner et al. book, Chapter data sets , CH24PR09 a ) Obtain the residuals for the A NOVA model and plot them against the fitted values . What does the plot suggest about the appropriateness of the model ? b ) Plot a normal probability plot of the residuals . Does the normality assumption seem reasonable ? fer to the previous question, and assume that the A NOVA model is suitable. a) Prepare AB interaction plotsoftheestimatedtreatmentmeans Yijk. separately for each level of Factor C. Does it appear that any interactions are present ? Any main effects'? b) Prepare AC interaction plotsoftheestimated treatmentmeans Yijk. separately for each level of Factor B. Does it appear that any interactions are present ? Any main effects? c ) Obtain the analysis of variance table. d) Explore form ally the presence of three-factor interactions, two-factor interac- tions, and main effects. State all of your hypotheses carefully, as well as your test statistics and the corresponding p-values for the tests. Summarize your conclusions ) To study the nature of the Factor A main effects and the BC interactions, it is desired to estimate the following comparisons (i) D1 = M1.. - M2. (ii ) D2 = 12 .. - M3 . . (iii ) D3 = M1. - M3.. (iv ) DA = M.11 - M .12 ( v) D5 = M.21 - M .22 (vi) L1 = DA - D5 Use the Bonferroni procedure with a 90 % family confidence coefficient to make the desired comparisons . State your findings f) Estimate D = /121 - /221 with a 95% confidence interval. Interpret the result