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 = 0.01. State your null and alternative hypotheses. State your decision for this test, and provide a conclusion based your decision.

Source df SS MS F Value Prob > F

Treatments 2 5373.216 2686.608 20.73 0.0001

Error 57 7387.2 129.6

Total 59 12,760.416