SCENARIO 11-8
a Physician and President of a Tampa Health

SCENARIO 11-8
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to
show the benefits of managed health care to an insurance company. The physician believes that
certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an
important factor in measuring the cost-effectiveness of physicians. To investigate this, the president
obtained independent random samples of 20 HMO physicians from each of 4 primary specialties -
General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and
recorded the total charges per member per month for each. A second factor which the president
believes influences total charges per member per month is whether the doctor is a foreign or USA
medical school graduate. The president theorizes that foreign graduates will have higher mean
charges than USA graduates. To investigate this, the president also collected data on 20 foreign
medical school graduates in each of the 4 primary specialty types described above. So information on
charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of
the 4 specialties. The results for the ANOVA are summarized in the following table. $$\begin{array} { l r r r r r } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Specialty } & 3 & 22,855 & 7,618 & 60.94 & 0.0001 \\\text { Med school } & 1 & 105 & 105 & 0.84 & 0.6744 \\\text { Interaction } & 3 & 890 & 297 & 2.38 & 0.1348 \\\text { Error } & 152 & 18,950 & & & \\\text { Total } & 159 & 42,800 & & & \\\hline\end{array}$$
-Referring to Scenario 11-8, what degrees of freedom should be used to determine the critical value of the F ratio against which to test for differences between the mean charges of foreign and
USA medical school graduates? a) numerator $d f = 1$ , denominator $d f = 159$
b) numerator $d f = 3$ , denominator $d f = 159$
c) numerator $d f = 1$ , denominator $d f = 152$
d) numerator $d f = 3$ , denominator $d f = 152$