Question

2) 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 bone mineral density. a) State the Hypothesis to show isoflavones have beneficial effects on bone mineral density. b) Choose a level of significance Use a = 0.05 for this problem. c) To test the hypothesis, a 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. At the end of the study period the researchers measured the bone mineral density in the femur (in grams per square centimeter). The data appear in the Kudzu worksheet of the HW4 data workbook on Moodle. Test the hypothesis using Excel. d) Draw a conclusion and report that in the context of the problem. e) Use Fisher’s LSD Test with a = 0.05 to determine which, if any, levels of dosage give significantly different densities. f) Assume that dosage is a random factor, i.e., the dosage levels represent a random sample of all possible dosage levels. Estimate the components of variance in bone density

data:

Control	Low dose	High dose
0.228	0.221	0.25
0.207	0.22	0.237
0.234	0.211	0.217
0.22	0.233	0.206
0.217	0.219	0.247
0.228	0.233	0.228
0.209	0.226	0.245
0.221	0.228	0.232
0.204	0.216	0.267
0.22	0.225	0.261
0.203	0.2	0.221
0.219	0.208	0.219
0.218	0.198	0.232
0.245	0.208	0.209
0.21	0.203	0.255

Answer 1

a)

b)

alpha = 0.05 is chosen

c)

anova single factor

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Control	15	3.283	0.218866667	0.000134267
Low dose	15	3.249	0.2166	0.000132114
High dose	15	3.526	0.235066667	0.000352352
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.003042978	2	0.001521489	7.377114535	0.001795859	3.219942293
Within Groups	0.008662267	42	0.000206244
Total	0.011705244	44

d)

p-value = 0.00179

p-value < 0.05

hence we reject the null hypothesis

we conclude that

isoflavones have beneficial effects on bone mineral density