15.33 Jumping and strong bones. Many studies suggest that exercise causes bones to get stronger. One study examined the effect of jumping on the bone density of growing rats. Ten rats were assigned to each of three treatments: a 60-centimeter “high jump,” a 30-centimeter “low jump,” and a control group with no jumping. Here are the bone densities

(in milligrams per cubic centimeter) after 8 weeks of 10 jumps per day:21 Group Bone density (mg/cm3)

Control 611 621 614 593 593 653 600 554 603 569 Low jump 635 605 638 594 599 632 631 588 607 596 High jump 650 622 626 626 631 622 643 674 643 650

(a) The study was a randomized comparative experiment. Outline the design of this experiment.

(b) Make side-by-side stemplots for the three groups, with the stems lined up for easy comparison. The distributions are a bit irregular but not strongly non-Normal. We would usually use analysis of variance to assess the significance of the difference in group means.

(c) Do the Kruskal-Wallis test. Explain the distinction between the hypotheses tested by Kruskal-Wallis and ANOVA.

(d) Write a brief statement of your findings.

Include a numerical comparison of the groups as well as your test result.