34. The article “The Responsiveness of Food Sales to Shelf Space Requirements” (J. Marketing Research, 1964:

63–67) reports the use of a Latin square design to investigate the effect of shelf space on food sales. The experiment was carried out over a 6-week period using six different stores, resulting in the following data on sales of powdered coffee cream (with shelf space index in parentheses):

Week 123 1 27 (5) 14 (4) 18 (3)

2 34 (6) 31 (5) 34 (4)

3 39 (2) 67 (6) 31 (5) Store 4 40 (3) 57 (1) 39 (2)

5 15 (4) 15 (3) 11 (1)

6 16 (1) 15 (2) 14 (6)

Week 456 1 35 (1) 28 (6) 22 (2)

2 46 (3) 37 (2) 23 (1)

3 49 (4) 38 (1) 48 (3) Store 4 70 (6) 37 (4) 50 (5)

5 9 (2) 18 (5) 17 (6)

6 12 (5) 19 (3) 22 (4)

Construct the ANOVA table, and state and test at level .01 the hypothesis that shelf space does not affect sales against the appropriate alternative.