In order to test the wear on four hyperalloys, a test piece of each alloy was extracted from each of the three positions of a test machine. The reduction of weight in milligrams due to wear was determined on each piece, and the data are given in Table 10.4.1.
Table 10.4.1 Loss in Weights Due to Wear Testing of Four Materials (in mg)

At α = 0.05, test the following hypotheses, regarding the positions as blocks:
(a) There is no difference in average wear for each material.
(b) There is no difference in average wear for each position.
(c) Interpret your final result and state any assumptions that were necessary to solve the problem.

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Position Type of alloy 274 241 195 235 270 241 273 236 218 227