Question

n an investigation into the effect of a high protein diet on vitamin C deficiency, we are told that 8 patients are given a high protein diet and 8 others are given a diet with a normal amount of protein for a week. The amount of a form of vitamin C in the blood is recorded in suitable units for each individual at the end of the trial. Summary values are given below.

--------------------------------High Protein Normal Protein

Mean                                            220.83----214.68

Standard Deviation                      8.59----- 7.74

Assume the two samples are drawn at random from normally distributed populations. Test, at the 5% significance level, whether the variability in the two underlying populations could be equal

Answer 1

null hypothesis:		σ21	=		σ22
Alternate Hypothesis:		σ21	≠		σ22

n1                  =		8
n2                  =		8
degree of freedom of numerator v1      =		7
degree of freedom of denominator v2 =		7
s12	=	73.7881
s22	=	59.9076

for 5 % level and given df critical values of F      =			0.200		&	4.995
Decision rule:reject Ho if test statistic F in critical region:			0.200		< F >	4.995

test stat F: =

s12/s22

=

1.232

as test statistic does not fall in rejection region ; we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that variability in the two underlying populations are different,