Consider the data from replicate I of Problem 9-3. Suppose that only a one-third fraction of this design with I = ABC is run. Construct the design, determine the alias structure, and analyze the data.

Problem 9-3.

An experiment was performed to study the effect of three different types of 32-ounce bottles (A) and three different shelf types (B)—smooth permanent shelves, end-aisle displays with grilled shelves, and beverage coolers—on the time it takes to stock ten 12-bottle cases on the shelves. Three workers (factor C) were employed in the experiment, and two replicates of a 33 factorial design were run. The observed time data are shown in the following table. Analyze the data and draw conclusions.

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Replicate I Replicate II Worker Bottle Type Permanent End Aisle Cooler Permanent End Aisle Cooler Plastic 3.45 4.14 5.80 3.36 4.19 5.23 4.07 4.38 5.48 3.52 4.26 4.85 28-mm glass 38-mm glass 1 4.20 4.26 5.67 3.68 4.37 5.58 Plastic 4.80 5.22 6.21 4.40 4.70 5.88 28-mm glass 4.52 5.15 6.25 4.44 4.65 6.20 38-mm glass 4.96 5.17 6.03 4.39 4.75 6.38 Plastic 4.08 3.94 5.14 3.65 4.08 4.49 4.99 4.04 4.08 4.59 28-mm glass 38-mm glass 4.30 4.53 4.17 4.86 4.85 3.88 4.48 4.90 3.