1. Hoffman, Jabaay, and Leuer did a study of pen- cil lead strength. They loaded pieces of lead of the same diameter (supported on two ends) in their centers and recorded the forces at which they failed. Part of their data are given here (in grams of bad applied at failure). 4H lead H lead 56.7, 63.8, 56.7 63.8, 49.6 99.2, 99.2, 92.1 106,0, 99.2 B lead 56.7, 63.8, 70.9 63.8, 70.9 (a) In applying the methods of this chapter in the analysis of these data, what model assump- tions must be made? Make three normal plots of these samples on the same set of axes and also make a normal plot of residuals for the one-way model as means of investigating the reasonableness of these assumptions. Com- ment on the plots. (b) Compute a pooled estimate of variance based on these three samples. What is the corre- sponding value of sp? (c) Use the value of s, that you calculated in (b) and make (individual) 95% two-sided con- fidence intervals for each of the three nean lead strengths, and y (d) Use s, and make (individual) 95% two-sided confidence intervals for each of the three differences in mean lead strengths, at Pag. and B (e) Suppose that for some reason it is desirable to compare the mean strength of B lead to the average of the mean strengths of 4H and H leads. Give a 95% two-sided confidence interval for the quantity(+)- (f) Use the P-R method of simultaneous confi- dence intervals and make simultaneous 95% two-sided confidence intervals for the three mean strengths, and How do the lengths of these intervals compare to the lengths of the intervals you found in part (c)? Why is it sensible that the lengths should be related in this way? (g) Use the Tukey method of simultaneous confi- dence intervals and make simultaneous 95% two-sided confidence intervals for the three differences in mean lead strengths, a and How do the lengths of these intervals compare to the lengths of the intervals you found in part (d)? (h) Use the one-way ANOVA test statistic and assess the strength of the evidence against Ho-Pall-My-in favor of H, not H Show the whole five-step format. () Make the ANOVA table corresponding to the significance test you carried out in part (h).