12.63 Do isoflavones increase bone mineral density? Kudzu is a plant that was imported to the United States from Japan and now covers over seven million acres in the South. The plant contains chemicals called isoflavones that have been shown to have beneficial effects on bones. One study used three groups of rats to compare a control group with rats that were fed either a low dose or a high dose of isoflavones from kudzu.²⁰ One of the outcomes examined was the bone mineral density in the femur (in grams per square centimeter). Here are the data:

Treatment	Bone mineral density (g/cm²)
Control	0.228	0.207	0.234	0.220	0.217	0.228	0.209	0.221
	0.204	0.220	0.203	0.219	0.218	0.245	0.210
Low dose	0.211	0.220	0.211	0.233	0.219	0.233	0.226	0.228
	0.216	0.225	0.200	0.208	0.198	0.208	0.203
High dose	0.250	0.237	0.217	0.206	0.247	0.228	0.245	0.232
	0.267	0.261	0.221	0.219	0.232	0.209	0.255

(a) Use graphical and numerical methods to describe the data.
(b) Examine the assumptions necessary for ANOVA. Summarize your findings.
(c) Run the ANOVA and report the results.
(d) Use a multiple-comparisons method to compare the three groups.
(e) Write a short report explaining the effect of kudzu isoflavones on the femur of the rat.