A Surgeon Is Interested in Studying the Range of Motion

Multiple Choice

A surgeon is interested in studying the range of motion of patients who have hip replacement surgery. He plans to have the patients evaluate their opinion of their range of motion; this will be a subjective score on a five-point scale. The low score, 1, will correspond to zero mobility, and the high score, 5, will correspond to full mobility. An objective measurement of the patient's range of motion will be taken by a physician and will be used as the response. The surgeon believes that the biological sex (male or female) of the patient will also be highly important.
It was impossible to force a balanced design, although an equal number of males and females were included and the design was crossed. A total of 60 observations were taken. A partial ANOVA table is provided here:

$\begin{array}{l}\begin{array}{lllll}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Score } & & 172 & & \\\text { Sex } & & 19 & & \\\text { Interaction } & & 48 & & \\\text { Error } & & 519 & & \\\hline\end{array}\\\text { C. Total }\end{array}$

Upon rejecting the null hypothesis for the test of an effect due to score, what is the correct interpretation of the true average mobility?

A) The true average mobility is different for all patients with different scores.
B) The true average mobility is not different for any of the scores.
C) The true average mobility is different for at least one pair of scores.
D) The true average mobility is different for all scores, but only for females or males-not both.