For Problem 8.5–12, do the following:
(a) Produce side-by-side boxplots and one-way ANOVA table using R; attach the plot and R output.
> treatment = c(rep("Carbo",7), rep("Whey",7), rep("CC", 7), rep("CW", 7))
> response = c(3,5,2,5,1,4,8, 5,3,5,4,7,4,5, 7,8,10,7,5,4,9, 11,9,15,9,12,10,5)
# Draw side-by-side boxplots:
> boxplot(response ~ treatment)
# One-way ANOVA F test:
> anova(lm(response ~ treatment))
(b) Do you reject the null hypothesis in the overall F test? How many pairwise comparisons of means can be done using Bonferroni t tests?
(c) For Carbohydrate (xCarbo = 4.00) vs. Creatine and whey (xCW = 10.14),
1) Calculate Bonferroni t test statistic.
2) Provide critical value for rejection region using both t table and R (attach code and output).
3) Compute Bonferroni adjusted p-value using R (attach code and output).
(d) Report Bonferroni adjusted p-values for all pairwise comparisons using the R built-in function below (attach output).
> pairwise.t.test(response, treatment, p.adjust.method="bonferroni")
12. Bodybuilders consume large volumes of dietary supplements, especially products that combine creatine with whey proteins, a waste product of cheese making. In a study to assess the impact of creatine and whey on strength and muscle fiber characteristics, 28 highly trained bodybuilders in their mid-20s were recruited for a 13-week dietary study. The researchers divided the volunteers into four groups, giving each man the same caloric bonus per day: a flavored drink containing a gram of supplement per kilogram of body weight. One supplement contained just carbohydrates, another just whey powder, and the last two a mix of creatine with either carbohydrates or whey. The experiment was conducted as a double-blind with neither the athletes nor the scientists knowing who received each supplement until the study was completed. Throughout, the men performed supervised resistance training three times a week and all experienced strength gains. Below are the data for increases in bench press totals in kilograms for the 28 bodybuilders.
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CHAPTER 8: Problems and Answers
Carbohydrate only
Whey Creatine and only carbohydrate
Creatine and whey
3 5 2 5 1 4 8
5 3 5 4 7 4 5
7 8 10 7 5 4 6
11 9 15 9 12 10 5
Do the data indicate that the combination of creatine and whey is significantly better than the other supplements? Use the Bonferroni-Holm test for mean separation, if necessary.
