Kudzu is a plant that was imported to the United States from

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. One of the outcomes examined was the bone mineral density in the femur (in grams per square centimeter). Researchers would like to test if the mean bone mineral density is different for the three different groups. Using the data set BoneMineralData, conduct an ANOVA test to determine if there is a difference in the means of the 3 groups. Use a level of significance of . Use this information to answer questions 1 through 5.

Solution

The data set are

1.The null and alternative hypotheses are

H₀: All the means are equal

H_a: At least one of the means differs

2. Using the R-command, we show that the data are normal or not

control=c(0.228,0.207,0.234,0.22,0.217,0.228,0.209,0.221,0.204,0.22,0.203,0.219,0.218,0.245,0.21)
high =c(0.25,0.237,0.217,0.206,0.247,0.228,0.245,0.232,0.267,0.261,0.221,0.219,0.232,0.209,0.255)
low =c(0.211,0.22,0.211,0.233,0.219,0.233,0.226,0.228,0.216,0.225,0.2,0.208,0.198,0.208,0.203)
par(mfrow=c(3,2))
hist(control, freq = FALSE, main=\"Histogram for Control\")
curve(dnorm(x, mean=mean(control), sd=sd(control)), col=\"blue\", lwd=2,add=TRUE)
lines(density(control),col = \"red\", lwd=2)
qqnorm (control, main = \"Normal Quantile Plot for Control\")
qqline (control)
hist(low, freq = FALSE, main=\"Histogram for Low Dose\")
curve(dnorm(x, mean=mean(low), sd=sd(low)), col=\"blue\", lwd=2,add=TRUE)
lines(density(low),col = \"red\", lwd=2)
qqnorm (low, main = \"Normal Quantile Plot for Low Dose\")
qqline (low)
hist(high, freq = FALSE, main=\"Histogram for High Dose\")
curve(dnorm(x, mean=mean(high), sd=sd(high)), col=\"blue\", lwd=2,add=TRUE)
lines(density(high),col = \"red\", lwd=2)
qqnorm (high, main = \"Normal Quantile Plot for High Dose\")
qqline (high)

These graphs show that the data are approximately normal for each group, the variances are equal for each group

3. THe test statistic is find by using Excel

The F-value is 7.71823 with df 2,42

4. The p-value is 0.001397

5. Reject the null. There is sufficient evidence to suggest that there is a difference in the means of one or more of the groups from the others.