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Question 12.139

fibercereal

23. The following table contains a random sample of breakfast cereals, along with their brands, whether or not they are high in fiber (at least 3 grams), and their nutritional rating. Use level of significance α=0.05 to perform the two-way ANOVA.

Cereal Brand Fiber Rating
Shredded Wheat Kellogg's High 68.2
All Bran Kellogg's High 59.4
Wheaties General Mills High 51.6
Total General Mills High 46.7
Nut'n Honey Kellogg's Low 29.9
Corn Flakes Kellogg's Low 45.9
Lucky Charms General Mills Low 26.7
Cocoa Puffs General Mills Low 22.7

12.4.23

H0: There is no interaction between brand (Factor A) and fiber (Factor B). Ha: There is interaction between brand (Factor A) and fiber (Factor B). Reject H0 if the p-value0.05. The p-value=0.888, which is not 0.05; therefore we do not reject H0. There is insufficient evidence of interaction between brand (Factor A) and fiber (Factor B) at level of significance α=0.05. H0: There is no brand (Factor A) effect. That is, the population means do not differ by brand. Ha: There is a brand (Factor A) effect. That is, the population means do differ by brand. Reject H0 if the p-value0.05. The p-value=0.045, which is 0.05; therefore we reject H0. There is evidence for a brand (Factor A) effect. Thus we can conclude at level of significance α=0.05 that there is a significant difference in mean nutritional ratings between Kellogg's cereals and General Mills cereals. H0: There is no fiber (Factor B) effect. That is, the population means do not differ by whether or not the cereal has fiber. Ha: There is a fiber (Factor B) effect. That is, the population means do differ by whether or not the cereal has fiber. Reject H0 if the p-value0.05. The p-value=0.006, which is 0.05; therefore we reject H0. There is evidence for a fiber (Factor B) effect. Thus we can conclude at level of significance α=0.05 that there is a significant difference in mean nutritional ratings between cereals with a high fiber content and cereals with a low fiber content.

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