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standard devil t deal of space in a recrill jUu Would gener in the samples were European American, 83%; Asian Am-es were your conclusions and the results (e) The percents of female s follows: European American s of female students in the sampl r con nk that we need to lity in the data will w using ANOVA to er. nese, 63%; Indian, 64%; and Hispanic Americancan, 67 c American, 79%Use on influences your in- elp bones. Kudzu is a plant tho in the South. The plant contains chem. Bon Japanese chisquare test to compare these proportioner 05) and discuss how this information inf cti e 5 pag 9. Give the degrees terpretation of the results that you have fn in table) or an exact 14.62 A natural product can help bones. Kudzu is deviation for these a u r cor 14.62 A natural was imported safet to the United States from Japan and now the F distribution covers that have been shown to have beneficial ne study used three groups of rats to compare therefor the sup lude? over seven million acres in the South. The pla lysis, describe the icals called isoflavones that have been shown to hae he ible for your con- effects on bones. O are quite similar? are quite simlara control group with rats that were fed either a low dose or the rest er to the previous dose of isoflavones from kudzu.1 One of the outcomes motions in some was the bone mineral density in the femur (in grams articipant carried centimeter). Here are the data:KUD s during a three- ded, participants Treatment emotions for the Control 0.228 0.207 0.234 0.220 7 0.228 0.209 0.221 responses were number of emo- ed per square TAB Bone mineral dessity (g/em2) Numbe 0.204 0.220 0.203 0.219 8 0.245 0.210 0.216 0.225 0.200 0.20818 0.208 0.203 0.267 0.261 0.221 0.219 0.232 0.209 0.255 of emo-Low nsity, an average Low dose 0.211 0.220 0.211 0.2339 0.233 0.226 0.228 to 6. At the end s were asked to High dose 0.250 0.237 0.217 0.206 0.247 0.228 0.245 0.232 different emo- summary of the (a) Use graphical and numerical methods to describe the data. (b) Examine the assumptions necessary for ANOVA. Summarize your findings. Recall mean (s 49.12 (22.33) (d) Use a multiple-comparisons met 43.98 59.99 (24.64) e) Run the ANOVA and report the results. groups. ) 39.77 (23.24) a multiple-comparisons method to compare the three 43,98 (22.02) (e) Write a short report explaining the effect of kudzui 59991246) 14.63 Promotions and the expected priceuced pric. 49.86 (21.60) ort report explaining the effect of kudzu isoflavones on the femur of the rat. 1463 Promotions and the expected price of a produc supermarket product is frequently offered at a espected price f a pu a product. If a do uct is frequently offered at a reduced pnce

Explanation / Answer

Here there are three groups control, low dose and high dose.

By using ANOVA we test mean effect of different groups.

ANOVA assumptions :

Let mu1 be the population mean of control.

mu2 be the population mean of low dose.

mu3 be the population mean of high dose.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3 Vs H1 : Atleast one of the mean is differ than 0.

Assume alpha = 5% = 0.05

This we can done using F-test.

test statistic F = MSB / MSE

ANOVA we can done using EXCEL.

steps :

First enter all the data in EXCEL sheet --> Data --> Data Analysis --> Anova : Single Factor --> ok --> Input Range : select all the range --> Grouped by : columns --> Alpha : 0.05 --> Output Range : select one empty cell --> ok

And the output is :

From the output,

Test statistic F = 7.08848

P-value = 0.002226

Fcritical = 3.2199

P-value < alpha (0.05)

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the mean is differ than 0.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 15 3.303 0.2202 0.000156 Column 2 15 3.239 0.215933 0.000132 Column 3 15 3.526 0.235067 0.000352 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.003027 2 0.001513 7.08848 0.002226 3.219942 Within Groups 0.008966 42 0.000213 Total 0.011993 44

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