History Kudzu is a plant that was imported to the United States from Japan and n

Question

History 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 soflavones from kudzu. One of the outcomes was the bone mineral density in the femur (in grams per square centimeter). Here are the data Control 0.229 0.207 0.234 0.220 0.217 0.228 0.209 0.221 Low Dose 0.214 0.220 0.211 0.233 0.219 0.233 0.226 0.228 Hlgh Dose 0.255 0.237 0.217 0.206 0.247 0.228 0.245 0.232 0.204 0.220 0.203 0.219 0.218 0.245 0.210 0.216 0.225 0.200 0.208 0.198 0.208 0.203 0.267 0.261 0.221 0.219 0.232 0.209 0.255 (a) Use numerical methods to describe the data. (Round your answers to four decimal places.) Control 15 Low Dose 15 High Dose 15 V02189 02161 0.2354 0.0116 00114 00191 Toa (c) Run the ANOVA and report the results. State the F statistic and the degrees of freedom. (Round your answers to two decimal places.) F 7.72

Explanation / Answer

b)

In a one way ANOVA, the samples must be independent of each other. As we have collected for three different treatments separately, so all the three sample data are independent of others. Also, the population variance of all the samples must be same. As we can see that the sample standard deviations are almost same, so we can assume that the population variances are also close. The normality of the data can be verified using the 6 sigma approach. Note that all the data lie within three standard deviation of the mean for each treatment. So, we would assume the data to be normally distributed.

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c)

The degree of freedom of freedom between groups is given as : DFG = k-1

While the degree of freedom of errors is given as : DFE = n-k

Where, 'n' is total number of observations,

and 'k' is number of treatments.

In this case, total number of observations = n = 15 x 3 = 45

and, number of treatments = k = 3

So, DFG = k - 1 = 2

and, DFE = n - k = 42

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