Taste-testers of new food products are presented with several competing food samples and asked to rate the taste of each on a 9-point scale (where 1 = "dislike extremely" and 9 = "like extremely"). In the Journal of Sensory Studies (June 2014), food scientists compared two different taste-testing protocols. The sequential monadic (SM) method presented the samples one-at-a-time to the taster in a random order, while the rank rating (RR) method presented the samples to the taster all at once, side-by-side. Consider the following experiment (similar to the one conducted in the journal): 50 consumers of apricot jelly were asked to taste test five different varieties. Half the testers used the SM protocol and half used the RR protocol during testing. In a second experiment, 50 consumers of cheese were asked to taste-test four different varieties. Again, half the testers used the SM protocol and half used the RR protocol during testing. For each product (apricot jelly and cheese), the mean taste scores of the two protocols (SM and RR) were compared. The results are shown in the accompanying tables.

a. Consider the five varieties of apricot jelly. Identify the varieties for which you can conclude that "the mean taste scores of the two protocols (SM and RR) differ significantly at a = .05."
b. Consider the four varieties of cheese. Identify the varieties for which you can conclude that "the mean taste scores of the two protocols (SM and RR) differ significantly at a = .05."
c. Explain why the taste-test scores do not need to be normally distributed for the inferences, parts a and b, to be valid.

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Apricot Jelly (Taste means) Varlety RR Cheese (Taste means) SM P-value Variety RR 6.4 6.7 5.4 6.4 6.1 SM P-value 4.4 5.3 4.7 6.7 .013 .065 6.8 5.2 A 5.9 B 5.6 488 .721 .983 .585 .499 6.9 5.3 .002 6.7 D 6.4 7.5 D .034