Health officials have recently expressed concern about problems associated with

Question

Health officials have recently expressed concern about problems associated with vitamin D deficiency among certain immigrants. Doctors have conjectured that such a deficiency could be related to the amount of fiber in a person’s diet. The chemical compound H-labeled 25-hydroxy-vitamin D3 (25(OH)D3) is the major circulating form of vitamin D, and its plasma half-life is intimately related to the body's vitamin D level. An experiment to compare plasma half-lives for two groups of health individuals, one placed on a normal diet and the other placed on a high-fiber diet, resulted in the following data

Normal Diet: 19.1 24.0 28.6 29.7 30.0 34.8

High-fiber 12.0 13.0 13.6 20.5 22.7 23.7

Does this data suggest that the average plasma half-life for persons placed on a normal diet exceeds the average half-life for those on a high fiber diet? Test the hypothesis using t-test and pooled data at Alfa =.05

Explanation / Answer

H0 : mu1 = mu2
Ha : mu1 > mu2

Test statistics:

x1= 27.7 , s1 = 5.4435, n1 = 6
x2 = 17.5833, s2 = 5.2943, n2 = 6

t = (x1 -x2)/Sp * sqrt(1/n1 + 1/n2)

Sp = sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2))
= sqrt(((6-1)* 5.4435^2 + ( 6-1)*5.2943^2)/(6+6-2))
= 5.3694

t = ( 27.7 - 17.5833)/5.3694 * sqrt(1/6 + 1/6)
= 1.0878

p value = .1511

Do not reject the null hypothesis

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