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? Run the test at a 5% level of significance, assuming the outcome is normally distributed. (enter 1 for “yes”, and 0 for “no”)

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

Answer 1

From the sample data, it is found that the corresponding sample means are:

Xˉ1=164.667
Xˉ2=165.333
Also, the provided sample standard deviations are:

s1=30.329
s2=29.139
and the sample size is n = 6. For the score differences we have

Dˉ =−0.667
sD=3.266

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μD= 0

Ha: μD < 0

This corresponds to a left-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=5.

Hence, it is found that the critical value for this left-tailed test is tc=−2.015, for α=0.05 and df=5.

The rejection region for this left-tailed test is R={t:t<−2.015}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

t= Dbar/sD/sqrt(n)= -0.667/3.266/\sqrt(6)= -0.5
(4) Decision about the null hypothesis

Since it is observed that t=−0.5≥tc =−2.015, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.3191, and since p=0.3191≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1 is less than μ2, at the 0.05 significance level. We don't have sufficient evidence to conclude that there is a significant increase in body weight following supplementation.

0 FOR N0