A Certain HMO Is Attempting to Show the Benefits of Managed

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMObelieves that certain types of doctors are more cost-effective than others. One theory is that Certification Levelis an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtainedindependent random samples of 20 physicians from each of the three certification levels-- Board certified (C) ;Uncertified, board eligible (E) ; and Uncertified, board ineligible (I) -- and recorded the total per member permonth charges for each (a total of 60 physicians) . In order to compare the mean charges for the three groups,the data will be subjected to an analysis of variance. The results of the ANOVA are summarized in thefollowing table. Take α = 0.01. Interpret the P-value of the ANOVA F test. $$\begin{array} { l r c c c c c } \text { Source df } & \text { SS } & \text { MS } & \text { F Value } & \multicolumn{2}{c} { \text { Prob > F } } & \\\hline \text { Treatments } & 2 & 3752.13 & 1876.065 & 20.73 & 0.0001 \\\text { Error } & 57 & 5158.5 & 90.5 & & \\\text { Total } & 59 & 8910.63 & & &\end{array}$$

A) The means of the total per member per month charges for the three groups of physicians differ at α = 0.01.
B) The model is not statistically useful (at α = 0.01) for prediction purposes.
C) The variances of the total per number per month charges for the three groups of physicians differ at α = 0.01.
D) The means of the total per member per month charges for the three groups of physicians are equal at α = 0.01.