Researchers compared protein intake among threegroups of postmenopausal women: (1) women eating astandard American diet (STD), (2) women eating a lacto-ovo-vegetarian diet (LAC), and (3) women eating a strictvegetarian diet (VEG). The mean ± 1 sd for protein intake(mg) is presented in Table 12.29.Table 12.29 Protein intake (mg) among three dietarygroups of postmenopausal womenGroupМeansdSTD75910LAC571310VEG4717*12.1 Perform a statistical procedure to comparethe means of the three groups using the critical-valuemethod.*12.2 What is the p-value from the test performed in Prob-lem 12.1?

Here, to check that: H0: μSTD =μLAC =μVEG vs H1 : H0 not true μSTD: Population mean STDμLAC : Population mean LAC μVEG: Population mean VEG The results were obtained as : Group meani sdi ni STD 75 9 10 LAC 57 13 10 VEG 47 17 6overallmean=n1×mean1+n2×mean2+n3×mean3(n1+n2+n3) = 61.61538462SSE=∑(ni-1)×(Sdi)2 =9×(9)2+9×(13)2+5×(17)2 = 3695SSR=∑nI(meani-overallmean)2 =10×(75– 61.61538462)2+10×(57– 61.61538462)2+6×(47– 61.61538462)2=3286.153846 ANOVA TABLE SOURCE DF SS MS F0 model 2 3286.153846 1643.076923 10.22754242 error 23 3695 160.6521739 total 25 7520.153846 The CRITICAL -Value is obtained as : As F0 > fcritical-value we reject H0 at 5 % level of significance That is there are significant differences in protein intake(mg) among 3 dietary groups.The P-value of the test is obtained as : P(X> | Fo=10.22754242 | )= 0.0007 As the P-value < 0.05 we reject the null hypothesis at 5% level of significance. That is there are significant differences in protein intake(mg) among 3 dietary groups.

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Researchers compared protein intake among three groups of postmenopausal women: (1) women eating a standard American diet (STD), (2) women eating a lacto- ovo-vegetarian diet (LAC), and (3) women eating a strict vegetarian diet (VEG). The mean ± 1 sd for protein intake (mg) is presented in Table 12.29.

Researchers compared protein intake among three groups of postmenopausal women: (1) women eating a standard American diet (STD), (2) women eating a lacto- ovo-vegetarian diet (LAC), and (3) women eating a strict vegetarian diet (VEG). The mean ± 1 sd for protein intake (mg) is presented in Table 12.29.

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Question

Researchers compared protein intake among three
groups of postmenopausal women: (1) women eating a
standard American diet (STD), (2) women eating a lacto-
ovo-vegetarian diet (LAC), and (3) women eating a strict
vegetarian diet (VEG). The mean ± 1 sd for protein intake
(mg) is presented in Table 12.29.
Table 12.29 Protein intake (mg) among three dietary
groups of postmenopausal women
Group
Мean
sd
STD
75
9
10
LAC
57
13
10
VEG
47
17
*12.1 Perform a statistical procedure to compare
the means of the three groups using the critical-value
method.
*12.2 What is the p-value from the test performed in Prob-
lem 12.1?

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