A Study Randomly Assigned Adult Subjects to Three Exercise Treatments

Multiple Choice

A study randomly assigned adult subjects to three exercise treatments: (1) a single long exercise period five days per week; (2) several ten-minute exercise periods five days per week; and (3) several ten-minute periods five days per week using a home treadmill. The study report contains the following summary statistics about weight loss (in kilograms) after six months of treatment:
$$\begin{array} { | l | l | l | l | } \hline \text { Treatment } & \text { Mean } & \text { Std. dev. } & \boldsymbol { n } \\\hline \text { (1) Long periods } & 10.2 & 4.2 & 37 \\\hline \text { (2) Multiple short periods } & 9.3 & 4.5 & 36 \\\hline \text { (3) Multiple short periods with treadmill } & 10.2 & 5.2 & 42 \\\hline\end{array}$$ The researchers want to contrast the long-period exercise regimen (1) with both short-period regimens (2 and 3) . What is the appropriate population contrast?

A)
$$L = \mu _ { 1 } + \mu _ { 2 } + \mu _ { 3 }$$
B)
$$L = \mu _ { 1 } - \mu _ { 2 } - \mu _ { 3 }$$
C)
$$L = \mu _ { 1 } - \frac { 1 } { 2 } \mu _ { 2 } - \frac { 1 } { 2 } \mu _ { 3 }$$
D) $$L = \frac { 1 } { 3 } \mu _ { 1 } - \frac { 1 } { 3 } \mu _ { 2 } - \frac { 1 } { 3 } \mu _ { 3 }$$