Osteoarthritis of the Knee Is a Degenerative Disease Causing Joint

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, and
decreased function. Usual treatment is a combination of physical therapy,
medication, and arthroscopic surgery. The arthroscopic surgery involves removal of
cartilage fragments and calcium crystals, or the smoothing of bones to eliminate
difficulties with joint motion. Arthroscopic surgery is widely used, but it is not clear
how, or even if it works. In a recent study patients were randomly assigned to two
treatment groups. Patients in the arthroscopic surgery group received standard
arthroscopic treatment plus physical therapy and medicine. Patients in the other
group received only physical therapy and medicine. Two years after treatment the
patients were evaluated using standard scales for pain, stiffness, and physical
function. Higher scores indicate increased pain, increased stiffness, and decreased
physical function. Pain score data from the study are summarized below. Graphical
displays of the data indicate that it is reasonable to assume that the two pain score
distributions are approximately normal. $$\begin{array}{l}\text { Pain Scores at } 24 \text { months }\\\begin{array} { | c | c | c | c | c | } \hline \text { Treatment group } & & \text { Mean } & \begin{array} { c } \text { Standard } \\\text { deviation }\end{array} & \begin{array} { c } \text { Sample } \\\text { size }\end{array} \\\hline \text { Arthroscopic } & & 68.8 & 18.5 & 88 \\\hline \text { Non-Arthroscopic } & & 63.8 & 19.8 & 80 \\\hline\end{array}\end{array}$$ (a) What null hypothesis and alternative hypothesis might be used in this setting to
compare mean pain rating for the two treatments?
(b) For your hypotheses in part (a), what is the associated P-Value?
(c) Given your results in parts (a) and (b), what would you conclude about the
difference between the two treatments? Be sure to give your answer in the context
of this study.