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

Supermarket, j

Bottle Design, I 1 2 3 4

A 16 14 1 6

B 33 30 19 23

C 23 21 8 12