A popular consumer staple was displayed in different locations in the

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.

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