A Study Randomly Assigned Adult Subjects to One of Three

Multiple Choice

A study randomly assigned adult subjects to one of 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:
$$\begin{array} { | l | c | c | c | } \hline\text { Treatment } & \text { Mean } & \text { Std. Dev. } & \boldsymbol { n } \\\hline \text { Long periods } & 10.2 & 4.2 & 37 \\\hline \text { Multiple short periods } & 9.3 & 4.5 & 36 \\\hline \text { Multiple short periods with treadmill } & 10.2 & 5.2 & 42 \\\hline\end{array}$$ Here is a partial ANOVA table based on these data:
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$$\begin{array}{l}\begin{array} { l | l r } &\text {Source }&\text {df }&\text {Sums of Squares }&\text {Mean Square}&\text { F-Ratio}&\\\hline\text {group }&&&20.032\\\text { Error} && & &21.8967\\\hline\text {Total }&\end{array}\end{array}$$ What is the alternative hypothesis for the ANOVA?

A) The population mean weight loss after six months is greatest with multiple short periods of exercise using a treadmill.
B) The population mean weight loss after six months is different for each of the three exercise conditions.
C) The population mean weight loss after six months is not the same for the three exercise conditions.
D) The population mean weight loss after six months is the same for all three exercise conditions.