A popular consumer staple was displayed in different locations in the same aisle of a grocery store to determine what, if any, effect different placement might have on its sales. The product was placed at one of three heights on the aisle - low, medium, and high - and at one of three locations in the store - at the front of the store, at the middle of the store, and at the rear of the store. The number of units sold of the product at various height and distance combinations was recorded each week for five weeks, and the following results were obtained:
Front Middle Rear
Low 125 185 126
143 170 136
150 170 129
138 195 136
149 162 147
Med 141 176 128
137 161 133
145 167 148
150 165 145
130 184 141
High 129 157 149
141 152 137
148 186 138
130 164 126
137 176 138
What effect does the product placement have on the sales?
Analyze the data with an analysis of variance. Perform all the necessary tests (including testing for treatment means, interaction and, if necessary, for main effects), and state the hypotheses and conclusions for all of them. When testing for interaction, make sure you explain what interaction means in the context of this problem.
Produce a profile plot of the mean number of items sold. Comment on this and relate it to your tests.
Perform any relevant comparison of means procedures.
State your recommendations on where the product should be placed.
Verify that the assumptions for the test that you perform are satisfied.