My company conducted a consumer preference study involving three
different bottle designs (A, B, and C) for a new product.  The study
was carried out using a randomized block experimental design. 
Specifically, four supermarkets were supplied with all three bottle
designs, which were priced the same. Below is the number of bottles of
each design sold in a 24-hour period at each supermarket. SST, SSB,
and SSE is calculated to be 586.1667, 421.6667, and 1.8333,
respectively.

a Could you help us by testing the null hypothesis H0 that no
differences exist between the effects of the bottle designs on mean
daily sales? Set a= .05.

b Could you help us by testing the null hypothesis H0 that no
differences exist between the effects of the supermarkets on mean
daily sales. Set a = .05. We are trying to conclude whether the
different supermarkets have different effects on mean sales?

c Could you then use Tukey simultaneous 95 percent confidence
intervals to make pairwise comparisons of the bottle design effects on
mean daily sales. We are trying to determine which bottle design(s)
maximize mean sales?

Results of a Bottle Design Experiment

			Supermarket
Bottle Design, 	1	2	3	4
A			16	14	1	6
B			33	30	19	23
C			23	21	8	12