Refer to Exercise 17.35.

a. Group the types of alloys such that alloys within a group have similar mean hardness scores.
b. Group the types of condensation methods such that alloys within a group have similar mean hardness scores.
c. Estimate the variation in the mean hardnesses due to the dentist.
d. Use the residuals from the fitted model to determine if there are any violations in the conditions necessary to conduct the tests of hypotheses in this experiment.

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Alloy Denst Method1 792 824 813 792 792 907 72 835 2 772 772 782 98 665 835 870 3 782 803 752 620 835 847 560 585 803 803 715 803 813 858 907 882 2 752 772 772 782 743 933 792 824 715 707 835 715 673 698 734 681 1 715 724 743 627 752 858 762 724 2 792 715 813 743 613 824 8 782 762 606 743 681 43 715 824 681 673 946 792 743 762 894 792 649 2 657 743 690 882 772 813 870 858 690 245 493 707 289 715 813 312 634 715 707 698 715 772 1048 870 2 649 724 803 665 752 824 933 835 3 724 627 42 483 405 536 405 312