# Refer to Exercise 17.35. a. Group the types of alloys such that alloys within a group have…

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.

e. Estimate the variation in the mean hardnesses due to the dentist.

e. 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.

Exercise 17.35

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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