A small pilot study is conducted to investigate the effect of a nutritional supp

Question

A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Use a paired t-test at a 5% level of significance. 1. df= 2. Critical Value= 3. Computed statistic= 4. Based on comparing the computed statistic to the critical value which of the following is (are) true? (4 points) a. There is significant evidence, alpha=0.05, to show that body weight increased following supplementation? b. There is not significant evidence, alpha=0.05, to show that body weight increased following supplementation? c. Statistically speaking the difference in initial weights and weights after 6 weeks is 0. d. b and c

Subject Initial Weight Weight after 6 Weeks 1 155 157 2 142 145 3 176 180 4 180 175 5 210 209 6 125 126

Explanation / Answer

ans=

It would be better to define what you're measuring. Apparently it's absolute weight loss (after - before), given your reported s.d. You haven't said whether you're testing for weight loss or weight gain, so I'll assume that you're interested in any weight change and use a two-tailed z test.

At the 0.05 level of significance, z = +/- 1.96. The 95% confidence interval about zero (no change) is
0 +/- 1.96 (3.27 / sqrt(6) ) = +/- 2.61

The mean change = +0.67, which is well within the bounds of the CI, so this is not a significant result at the 0.05 level of significance.

Alternatively,
p = 1 - { CDF(0.67 / (3.27 / sqrt(6)) ) - CDF(-0.67 / (3.27 / sqrt(6)) ) }
= 1 - (0.6915 - 0.3085) = 0.617
so that the result is only significant at the 0.6 level of significance.
m
and the null hypothesis is that there is no change, so.27 /
z = (0.67 - 0) / (3.27 / sqrt(6) ) = 0.5

ther no significant increase in body weight following supplementati on mu=0

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