A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid 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 shows the number of bottles of each design sold in a 24-hour period at each supermarket. Using these data, it is determined that SST = 586.1667, SSB = 421.5667, and SSE = 1.8333.
Supermarkets, j
Bottle Design, i 1 2 3 4
A 16 14 1 6
B 33 30 19 23
C 23 21 8 12
a) Test the null hypothesis H_{o} that no differences exist between the effects of the bottle designs on mean daily sales. Set α = 0.05. Can we conclude that the different bottle designs have different effects on sales?
b) Test the null hypothesis H_{o} that no differences exist between the effects of the supermarkets on mean daily sales. Can we conclude that the different bottle designs have different effects on mean sales?