Customer portfolio analyses provide retailers with data on customer characteristics, including expenditure patterns. Based on this information, retailers can make marketing and operational adjustments to improve their market position. ABC Foods, a large supermarket chain, conducted a survey of the average weekly expenditures of 542 randomly selected residents in a large metropolitan market. The customers were classified as Loyal to ABC, New to ABC, Defectors from ABC, Loyal to competitors, and Unaffiliated. The average weekly expenditure data are summarized in the following table.

a. Suppose that an ANOVA is to be performed to compare the average weekly expenditures for the different customer types. State precisely the ANOVA model. Is customer type a fixed-effects factor or a random-effects factor?
b. Using the summary statistics given in the table, determine the ANOVA table for the model in part (a).
c. Test whether the five customer types differ significantly in average weekly expenditures.
d. Use Scheffe's method to locate any significant differences between pairs of means. (Use α = .05.)

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Customer Type Loyal to ABC New to ABC Defectors from ABC Loyal to competitors Avg. Weekly Expenditure (SD) $75 ($13) S65 ($10) $82 ($14) $93 ($17) $82 ($15) Sample Size 25 173 233