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-value≤ 0.05. 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-value≤ 0.05. 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-value≤ 0.05. 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.