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:
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$$\begin{array} { | l | c | c | c | } \hline \text { Treatment } & \text { Mean } & \text { Std. Dev. } & \boldsymbol { n } \\\hline \text { Long periods } & 10.2 & 4.2 & 37 \\\hline \text { Multiple short periods } & 9.3 & 4.5 & 36 \\\hline \text { Multiple short periods with treadmill } & 10.2 & 5.2 & 42 \\\hline\end{array}$$ Here is a partial ANOVA table based on these data:
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$$\begin{array}{l}\begin{array} { l | l r } &\text {Source }&\text {df }&\text {Sums of Squares }&\text {Mean Square}&\text { F-Ratio}&\\\hline\text {group }&&&20.032\\\text { Error} && & &21.8967\\\hline\text {Total }&\end{array}\end{array}$$ The ANOVA procedure relies on three important assumptions to be valid:
(1) The data are independent random samples.
(2) The populations are Normally distributed or the sample sizes are large enough.
(3) The populations have the same standard deviation σ .
In the case of this ANOVA test, which of the following statements is correct?

A) Assumption (1) is the only assumption not satisfied.
B) Assumption (2) is the only assumption not satisfied.
C) Assumption (3) is the only assumption not satisfied.
D) All three test assumptions are satisfied.