Question

Preliminary data analyses indicates that use of a paired Wilcoxon signed-rank test is reasonable. Perform the hypothesis test by using a paired Wilcoxon signed-rank test. Assume that the null hypothesis is Ho:u1=u2

In a study of the effectiveness of physical exercise in weight reduction, 12 subjects followed a program of physical exercise for two months. Their weights (in pounds) before and after this program are shown in the following table.

  

before	162	190	188	152	148	127	195	164	175	156	180	136
after	157	194	179	149	135	130	183	168	168	148	170	138

  

At the 5% significance level, do the data provide sufficient evidence to conclude that the exercise program is effective in reducing weight?

Answer 1

Solution:

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: the exercise program is not effective in reducing weight.

Alternative hypothesis: Ha: the exercise program is effective in reducing weight.

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

We take difference as before minus after.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 4.5

Sd = 6.3461

n = 12

df = n – 1 = 11

α = 0.05

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (4.5 – 0)/[ 6.3461/sqrt(12)]

t = 2.4564

The p-value by using t-table is given as below:

P-value = 0.0159

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the exercise program is effective in reducing weight.