Researchers Examined the Effect of Phosphate Supplementation on Bone Formation

Short Answer

Researchers examined the effect of phosphate supplementation on bone formation in six healthy adult dogs. For each dog, bone formation was measured twice: once after 12 weeks of phosphate supplementation and once after a 12-week control period. The results in percent bone growth per year are shown below. Do the data provide evidence that phosphate supplementation significantly stimulates bone formation?
$$\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Dog ID } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Control } & 1.73 & 3.37 & 3.59 & 2.05 & 1.86 & 3.60 \\\hline \text { Phosphate } & 8.16 & 4.58 & 3.98 & 5.24 & 3.04 & 7.03 \\\hline\end{array}$$
The data are analyzed using the Wilcoxon signed rank test. If the responses have a continuous distribution that is not affected by the different treatments, what is the mean value of W⁺?