The quality control department of a fabric finishing plant is studying the effects of several factors on dyeing for a blended cotton/synthetic cloth used to manufacture shirts. Three operators, three cycle times, and two temperatures were selected, and three small specimens of cloth were dyed under each set of conditions. The finished cloth was compared to a standard, and a numerical score was assigned. The results are shown in the following table.

(a) State and test the appropriate hypotheses using the analysis of variance with α = 0.05.

(b) The residuals may be obtained from e_ijkl = yÌ…_ijkl €“ yÌ…_ijk.. Graphically analyze the residuals from this experiment.

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Temperature 300° 350° Operator Operator Cycle Time 2 3 3 23 27 31 24 38 34 40 24 28 32 23 36 36 25 26 28 28 35 39 36 34 33 37 34 34 50 35 38 34 39 38 36 36 39 35 35 36 31 28 35 26 26 36 28 24 35 27 29 37 26 27 34 25 25 34 34