Test a Hypothesis Regarding Three or More Means Using One $\alpha = 0.01$

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent 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 per month 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 the following table. Take $\alpha = 0.01$ . Interpret the $\mathrm { P }$ -value of the ANOVA F test.

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