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. The table below 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.
a Test the null hypothesis H0 that no differences exist between the effects of the bottle design on mean daily sales. Set a _ .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 a _ .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?
Results of a Bottle Design Experiment
Bottle Design, I 1 2 3 4
A 16 14 1 6
B 33 30 19 23
C 23 21 8 12
The solution contains detailed explanation of testing hypotheses using the five-step procedures.