Three different chemicals are compared on their ability to make fabric stain-resistent. Four bolts of cloth, manufactured weeks apart, are used. Because the results are expected to vary from bolt of cloth to bolt, three small samples are cut from each bolt and a different chemical is applied to each. The

(a) Provide a decomposition for the observations from this randomized block experiment.
(b) Find the sum of squares for each array.
(c) Determine the degrees of freedom by checking the constraints for each array.

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Block Treatment 1 5 1201 8 15 813 5 12 01