The following study is from Oehlert (2000). Dental fillings made from gold can vary in hardness depending on how the metal is treated prior to its placement in the tooth. Two factors thought to influence the hardness are the gold alloy and the condensation method. In addition, some dentists performing the dental work are better at some types of filling than others. Five dentists were randomly selected and agreed to participate in the experiment. Each dentist prepared 24 fillings (in random order), one for each of the combinations of condensation method (three levels) and type of alloy (eight levels). The levels of condensation and type of alloy are the only levels of interest to the researchers. The fillings were then measured for hardness using the Diamond Pyramid Hardness Number (big scores are better). The data are contained in the following table:

a. Write an appropriate linear statistical model for this experiment. Identify all the terms in your model, and state all the conditions that are imposed on these terms.
b. Display a complete analysis of variance table, including expected mean squares, F tests, and p-values.
c. Is there significant evidence of an interaction between condensation method and type of alloy?

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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