Question

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 α = 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

Answer 1

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State your null and alternative hypotheses.

Null hypothesis, Ho: Certification Level is NOT an important factor in measuring the cost-effectiveness of physicians

Alternate hypothesis, Ha: Certification Level is an important factor in measuring the cost-effectiveness of physicians

Decision:

Since p-value in table of 0.0001 is less than our given alpha of .01 we will reject the null hypotheis

Conclusion based on Decision:

Yes,  Certification Level is an important factor in measuring the cost-effectiveness of physicians.