Question

-Identify why you choose to perform the statistical test (Sign test, Wilcoxon test, Kruskal-Wallis test).

-Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.

-Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

-Find the critical value(s) and identify the rejection region(s).

-Find the appropriate standardized test statistic. If convenient, use technology.

-Decide whether to reject or fail to reject the null hypothesis.

-Interpret the decision in the context of the original claim.

A weight-lifting coach claims that weight-lifters can increase their strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The results are listed below. Use the Wilcoxon signed-rank test to test the claim that the vitamin E supplement is effective in increasing athletes' strength. Use α = 0.05.

Athlete	1	2	3	4	5	6	7	8	9
Before	185	241	251	187	216	210	204	219	183
After	195	246	251	185	223	225	209	214	188

Answer 1

NULL HYPOTHESIS H0: the vitamin E supplement is effective in increasing athletes' strength i.e Md( Before)= Md(After)

ALTERNATIVE HYPOTHESIS HA: the vitamin E supplement is NOT effective in increasing athletes' strength i.e Md(Before)<Md(After) (Left tailed test)

alpha= 0.05

W-value: 4.5
Mean Difference: -39.75
Sum of pos. ranks: 4.5
Sum of neg. ranks: 31.5

Z-value: -1.8904 (nb. N too small)

Sample Size (N): 8

Result 1 - Z-value

The Z-value is -1.8904. However, the size of N (8) is not large enough for the distribution of the Wilcoxon W statistic to form a normal distribution. Therefore, it is not possible to calculate an accurate p-value.

Result 2 - W-value

The W-value is 4.5. The critical value of W for N = 8 at p≤ 0.05 is 5. Therefore, the result is significant at p≤ 0.05. We reject the null hypothesis.

We therefore conclude that vitamin E supplement is effective in increasing athletes' strength.