Do consumers react favorably to products with ambiguous colors or names? Marketing Professors E. G. Miller and B. E. Kahn investigated this phenomenon in the Journal of Consumer Research (June 2005). As a "reward" for participating in an unrelated experiment, 100 consumers were told they could have some jelly beans available in several cups on a table. Half the consumers were assigned to take jelly beans with common descriptive flavor names (e.g., watermelon green), while the other half were assigned to take jelly beans with ambiguous flavor names (e.g., monster green). Within each group, half of the consumers took the jelly beans and left (low cognitive load condition), while the other half were distracted with additional questions designed to distract them while they were taking their jelly beans (high cognitive load condition). Consequently, a 2 × 2 factorial experiment was employed- with Flavor Name (common or ambiguous) and Cognitive Load (low or high) as the two factors-with 25 consumers assigned to each of four treatments. The dependent variable of interest was the number of jelly beans taken by each consumer. The means and standard deviations of the four treatments are shown in the accompanying table.

a. Calculate the total of the n = 25 measurements for each of the four categories in the 2x2 factorial experiments.
b. Calculate the correction for mean, CM. (See Appendix C for computational formulas.)
c. Use the results of parts a and b to calculate the sums of squares for Load, Name, and Load × Name interaction.
d. Calculate the sample variance for each treatment. Then calculate the sum of squares of deviations within each sample for the four treatments.
e. Calculate SSE.
f. Now that you know SS(Load), SS(Name), SS(Load X Name), and SSE, find SS(Total).
g. Summarize the calculations in an ANOVA table.
h. The researchers reported the F-value for Load x Name interaction as F = 5.34. Do you agree?
i. Conduct a complete analysis of these data. Use α = .05 for any inferential techniques you employ. Illustrate your conclusions graphically.
j. What assumptions are necessary to ensure the validity of the inferential techniques you used? State them in terms of this experiment.

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Ambiguous Commorn MeanStd. Dev. Mean Std. Dev. Low load High load 18.0 6.1 15.0 9.5 7.8 6.3 9.5 10.0