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Nutrition 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  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 familywise error rate of

(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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Which Delivery Method Is Best? At a community college, the mathematics department has been experimenting with four different delivery mechanisms for content in their Intermediate Algebra courses. One method is the traditional lecture (method I), the second is a hybrid format in which half the class time is online and the other half is face-to-face (method II), the third is online (method III), and the fourth is an emporium model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (method IV). To assess the effectiveness of the four methods, students in each approach are given a final exam with the results shown next. Do the data suggest that any method has a different mean score from the others?

(a) What is the response variable in this study? Is it quantitative or qualitative?

(b) What is the factor in this study? How many levels does it have?

(c) Write the null and alternative hypotheses.

(d) State the requirements that must be satisfied to use the oneway ANOVA procedure.

(e) Assuming the requirements stated in part (d) are satisfied, use the following StatCrunch output to test the hypothesis of equal means at the  level of significance.

(f) Shown are side-by-side boxplots drawn in StatCrunch of each delivery method. Do these support the results obtained in part (e)?

(g) Interpret the -value.

(h) Verify the residuals are normally distributed.

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Construct a correlation matrix for the seven stock market indexes around the world. Describe what you find. That is, what indicators seem to be most strongly related to other indicators? Now focus on the three American stock market indicators. Which pair of these stock indicators is most correlated? Develop a regression model to predict the DJIA by the Nikkei 225. How strong is the model? Develop a regression model to predict the DJIA by the Hang Seng. How strong is the model? Develop a regression model to predict the DJIA by the IPC. How strong is the model? Compare the three models.

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Attention Deficit Hyperactivity Disorder Researchers studied the effect that varying levels of Ritalin and Adderall had on a child’s ability to follow rules when the child is diagnosed with attention deficit hyperactivity disorder (ADHD). They randomly assigned children to one of five treatment groups: placebo, 10 mg of Ritalin, 17.5 mg of Ritalin, 7.5 mg of Adderall, or 12.5 mg of Adderall twice a day. They recorded a score that indicated the child’s ability to follow rules, with a higher score indicating a higher ability to follow rules. The following data are based on their study, “A Comparison of Ritalin and Adderall: Efficacy and Time-Course in Children with Attention Deficit/ Hyperactivity Disorder,” Pediatrics, Vol. 103, No. 4.

(a) The data was collected using a completely randomized design. Explain what this means.

(b) What is the response variable in this study? What explanatory variable was controlled and fixed at five levels?

(c) The children were randomly assigned to one of five treatment groups. What role does randomization play in this study?

(d) What are the null and alternative hypotheses in this study?

(e) Test the null hypothesis that the mean score for each treatment is the same at the  level of significance. Note: The requirements for a one-way ANOVA are satisfied.

(f) If the null hypothesis is rejected in part (e), use Tukey’s test to determine which pairwise means differ using a familywise error rate of

(g) Draw boxplots of the five treatment levels to support the analytic results obtained in parts (e) and (f).

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