A managerial decision problem. A direct-mail company assembles and stores paper products (envelopes, letters, brochures, order cards, etc.) for its customers. The company estimates the total number of pieces received in a shipment by estimating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton, or whether it is worth the extra time required to pull a few pieces from several cartons. To aid management in making a decision, eight brochures were pulled from each of five cartons of a typical shipment and weighed. The weights (in pounds) are shown in the table.

a. Identify the response, factor(s), treatments, and experimental units.

b. Do these data provide sufficient evidence to indicate differences in the mean weight per brochure among the five cartons?

c. What assumptions must be satisfied in order for the test of part b to be valid?

d. Use Tukey’s method to compare all pairs of means, with  = .05 as the overall level of significance.

e. Given the results, make a recommendation to management about whether to sample from one carton or from many cartons.

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