Researchers Sharon Peterson and Madeleine Sigman-Grant wanted to compare the overall nutrient intake of American children (ages 2 to 19) who exclusively use lean meats, mixed meats, or higher-fat meats. The data given on the next page represent the daily consumption of calcium (in mg) for a random sample of eight children in each category and are based on the results presented in their article "Impact of Adopting Lower-Fat Food Choices on Nutrient Intake of American Children," Pediatrics, Vol. 100, No. 3.

(a) The data was collected using a cohort observational study.
Explain what this means.
(b) What is the response variable in this study?
(c) What are the null and alternative hypotheses in this study?
(d) Test the null hypothesis that the mean calcium for each category is the same at the a = 0.05 level of significance.
Note: The requirements for a one-way ANOVA are satisfied.
(e) If the null hypothesis is rejected in part (d), use Tukey's test to determine which pairwise means differ using a family wise error rate of a = 0.05.
(f) Draw boxplots of the three treatment levels to support the analytic results obtained in parts (d) and (e).
(g) Can any statements of causality between meat consumption and consumption of calcium be made based on the results of this study? Explain.

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Mixed Meats Higher-Fat Meats Lean Meats 844.2 897.7 843.4 908.1 745.0 862.2 773.1 948.8 790.5 876.5 823.6 836.6 790.8 812.0 871.6 758.9 945.9 847.2 810.7 859.4 772.0 790.6 920.2 851.3