Grocery Store

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

 

Medium

 

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?

For this you should:

i) 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 precisely what interaction means in the context of this problem.

ii) Produce a profile plot of the mean number of items sold. Comment on this and relate it to your tests.

iii) Perform any relevant comparison of means procedures.

iv) State your recommendations on where the product should be placed.