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 pooled standard deviation for the entire data set is 4.30 kg. The researchers want to contrast the long-period exercise regimen (1) with both short-period regimens (2 and 3) . What is the 95% confidence interval for this contrast?

A) 0.45 ± (1.984) (4.30)
$$\left( \sqrt { \frac { 1 } { 37 } + \frac { 1 } { 36 } + \frac { 1 } { 42 } } \right)$$
B) 0.9 ± (1.984) (4.30)
$$\left( \sqrt { \frac { 1 } { 37 } - \frac { 0.25 } { 36 } - \frac { 0.25 } { 42 } } \right)$$
C) 0.45 ± (1.984) (4.30)
$$\left( \sqrt { \frac { 1 } { 36 } + \frac { 0.25 } { 37 } + \frac { 0.25 } { 42 } } \right)$$
D) 0.9 ± (1.984) (4.30) $$\left( \sqrt { \frac { 1 } { 37 } - \frac { 1 } { 36 } - \frac { 1 } { 42 } } \right)$$