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:

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

What is the correct null hypothesis for the test of an effect due to the patient's subjective score?

A) H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
B) H₀: At least one pair is different
C) H₀: μ₁= μ₂ = μ₃ = μ₄= μ₅ = 0
D) H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅