A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid laundry detergent was carried out using a randomized block experimental design, with supermarkets as blocks. Specifically, four supermarkets were supplied with all three bottle designs, which were priced the same. Table 11.10 gives the number of bottles of each design sold in a 24-hour period at each supermarket. If we use these data, SST, SSB, and SSE can be calculated to be 586.1667, 421.6667, and 1.8333, respectively.
TABLE 11.10
Results of a Bottle Design Experiment

a. Test the null hypothesis H0 that no differences exist between the effects of the bottle designs on mean daily sales. Set α = .05. Can we conclude that the different bottle designs have different effects on mean sales?
b. Test the null hypothesis H0 that no differences exist between the effects of the supermarkets on mean daily sales. Set α = .05. Can we conclude that the different supermarkets have different effects on mean sales?
c. Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the bottle design effects on mean daily sales. Which bottle design(s) maximize mean sales?

Supermarket, i Bottle Design, 1 2 16 33 30 19 23 23 21 4 14 8 12