1. Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study exami- ned the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low jump condition (the jump heigth was 30 centimeters), and a high jumping condition (60 cm). In each group there were 10 rats, ie. we had 30 statistical units altogether. After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (mg/m3) was measured. Does exercise have an eect on the bone density? Write down the hypothesis and interpret the result. Control Lawjimp nghjimp Group Levene's Test for Homogeneity of Variance (center = median) Df F value Pr(>F) group 2 0. 492 0. 6168 27 > > m. rat.1 summary (m. rat . 1) Df Sum Sq Mean Sq F value Pr (>F) group 2 7434 3717 7. 978 0. 0019 ** Residuals 27 12579 466 V > oneway . test (density group, data=rat) One-way analysis of means (not assuming equal variances) data: density and group F = 8.8164, num df = 2.000, denom df = 17.405, p-value = 0. 002268Tukey multiple comparisons of means 95%% family-wise confidence level $group diff 1wr upr p adj Highjump-Control 37.6 13. 66604 61.533957 0. 0016388 Lowjump-Control 11.4 -12. 53396 35.333957 0. 4744032 Lowjump-Highjump -26.2 -50. 13396 -2. 266043 0. 0297843 Pairwise comparisons using t tests with pooled SD data: p1$density and p1$group Control Highjump Highjump 0. 0018 Lowjump 0.7437 0. 0343 P value adjustment method: bonferroni # No equal variances assumed n means variances Control 10 601 749 Highjump 10 639 275 Lowjump 10 612 374 diff ci. lo ci.hi t df P Highjump-Control 38 11 63.9 3.7 15 .01 Lowjump-Control 11 -16 38.7 1.1 16 .54 Lowjump-High jump -26 -47 -5.6 3.3 18 .01