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Suppose that the experimenters are interested in the pairwise difference of the effects for factor 𝐴.

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Week 4 Quiz 1 Problem 1 (Popcorn Microwave Experiment) (10 points). The experiment was run by Jianjian Gong, Chongqing Yan, and Lihua Yang in 1992 to compare brands of microwave popcorn. The percentage, rather than number, of successfully popped kernels for each package was selected as the response variable. There are three treatment factors but only two of them will be considered here:

Factor 𝐴: brand, three levels with two national brands and one local brand Levels 1 and 2: two national brands; Level 3: local brand

Factor 𝐡: power of the microwave oven with two levels (500 and 625W).

Suppose that the experimenters are interested in the pairwise difference of the effects for factor 𝐴. Find the simultaneous 96% (this is not a typo) confidence interval of 𝛼∗ − 𝛼∗ with the Scheffé

1 2

method, and explain what this interval tells you. You need to present the corresponding formulas, plug in numbers, and obtain the final answers. Your calculation should be based on the two- way complete model and the following numbers:

π‘Ž = 3, 𝑏 = 2, 𝑛 = 36, π‘Ÿ = 6 = π‘Ÿπ‘–π‘—, π‘šπ‘ πΈ = 155

 

𝑦̅11βˆ™ = 76.0, 𝑦̅12βˆ™ = 76.6, 𝑦̅21βˆ™ = 67.0, 𝑦̅22βˆ™ = 75.8, 𝑦̅31βˆ™ = 63.0, 𝑦̅32βˆ™ = 74.8

 

Week 4 Quiz 1 Problem 2 (18 points). The experiment has two crossed factors 𝐴 and 𝐡 with the same number of replicates for each treatment combination. With the ANOVA tables from different models:

 

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