Consider the three-factor experiment in Problem 5-17 and assume that operators were selected at random. Find an approximate 95 percent confidence interval on the operator variance component.

Problem 5-17

The quality control department of a fabric finishing plant is studying the effect of several factors on the dyeing of cotton—synthetic cloth used to manufacture men's 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 follow. Analyze the data and draw conclusions. Comment on the model's adequacy.

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Temperature 300° 350° Operator Operator Cycle Time 1 3 1 2 3 23 27 31 24 38 34 40 24 28 32 23 36 36 25 26 29 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 60 24 35 27 29 37 26 27 34 25 25 34 24