Wilcoxon Rank Sum Test Question

2. Intermittent fasting (IF) consists of repetitive bouts of short-term fasting. It is of potential interest
because it may provide a simple tool to improve insulin sensitivity in individuals with insulin resistance.
(the latter increases the likelihood of type diabetes and heart disease). An article reported on a study in
which resting energy expenditure (kcal/d) was determined for a sample of n=8 subjects both while on an
IF regimen and while on a standard diet. The authors of the article provided the data:

Subject 1 2 3 4 5 6 7 8
IF REE 1753.7 1604.4 1576.5 1279.7 1754.2 1695.5 1700.1 1717.0
Std REE1755.0 1691.1 1697.1 1477.7 1785.2 1669.7 1901.3 1735.3

Test there is any difference between true average REE for the IF diet and that for the standard diet.
Answer: p-value<0.05

Ho: M1=M2
Ha: M1 doesnt equal M2

To answer this question I used the Wilcoxon Rank-Sum Test. I ranked the values from 1-16 and then I found the test statistic to be 23 using eqn: T= S- (n*(n+1)/2)

I used the critical values table for WRST and fo m=8 and n=8 found a c -value of 84. I'm a little confused on what the test statistic is saying? The P(W> 84)=0.052. So does this mean with a critical value of 84, there is a probablity of 0.052 that these medians are the same? Therefore I should coclude that we reject the null hypothesis and there is a difference between the medians of the two groups? ALso I thought I would have to double the probablity because it is a two-sided test?