14.5. Consider the three-stage nested design shown in Figure 14.5 to investigate alloy hardness. Using the data that follow, analyze the design, assuming that alloy chemistry and heats are fixed factors and ingots are random. Use the restricted form of the mixed model.

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Heats 1 Alloy Chemistry 1 2 3 Ingots 1 2 1 2 1 2 48 40 27 27 95 69 65 78 63 30 67 47 54 45 Alloy Chemistry 2 Heats 1 2 3 3 Ingots 1 2 1 2 1 2 22 23 83 55 75 61 35 10 39 62 64 77 42