Tablet hardness is one comparative measure for different formulations of the same drug product; some combinations of ingredients (in addition to the active drug) in a formulation give rise to harder tablets than do other combinations. Suppose that three batches of a formulation are randomly selected for examination. Three different 1-kg samples of tablets are randomly ­selected from each batch, and seven tablets are randomly selected for testing from each of the 1-kg samples. The hardness readings are given here.

a. Identify the design.
b. Give an appropriate model with assumptions.
c. Give the sources of variability and degrees of freedom for an AOV.
d. Perform an analysis of variance, and draw conclusions about the tablet hardness data for the formulation under study. Use α = .05.

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Batch 1 Batch 2 Batch 3 Sample 1 85 94 95 108 117 10 7 81 72 98 100 106 108 85 706 91 90 10 103 100 78 80 99 68 832 85 88 9 104 100 117 85 7275 76 87 96 09 109 93 96 93 08 02 105 76 78 74