Question: A study of cardiovascular risk factors compared runners who averaged at least 15 miles per week with a control group described as “generally sedentary”. Both men and women were included in the study. There were 20 subjects in each of the 4 combinations of gender (factor A) and running status (factor B). One of the variables measured was the heart rate after 6 minutes of exercise on a treadmill. The data are in the file Cardio_2008.JMP.

a. State the statistical model for the analysis appropriate for the study and define all parameters in the model.

b. What are the assumptions for the analysis? How would you verify the assumptions?

c. Using JMP, obtain the ANOVA table.

d. Is there a significant interaction? State the null and alternative hypotheses in terms of “no interaction” and “interaction”, value of the F test statistic, p-value (http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/pvalues.htm#rfdist) and conclusion.

e. Is the interaction orderly or disorderly? Use a profile plot to justify your conclusion. Can we test for the main effects of gender and running status on heart rate? Explain.

f. Describe what an interaction between gender and running status would mean in the context of the problem.

g. Is there a significant difference between the male and females in terms of their mean heart rates (i.e. is there a significant gender effect)? State the null and alternative hypotheses in terms of the appropriate parameters and in terms of “no effect of gender” and “effect of gender”, value of the F test statistic, critical value and thus rejection region (http://www.psychstat.missouristate.edu/introbook/fdist.htm)and conclusion.

h. Is there a significant difference between the runners and sedentary individuals in terms of their mean heart rates (i.e. is there a significant exercise/running effect)? State the null and alternative hypotheses in terms of the appropriate parameters and in terms of “no effect of running” and “effect of running”, value of the F test statistic, p-value (http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/pvalues.htm#rfdist) and conclusion.