Instruction 11-10
the CEO of a Large Australian Health Fund

question 23

Multiple Choice

Instruction 11-10
The CEO of a large Australian health fund is attempting to show the benefits of managed health care to an insurance underwriting company. The CEO believes that certain types of doctors are more cost-effective than others. One theory states that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the CEO obtained independent random samples of 20 physicians from each of four primary specialties - General Practice (GP) , Internal Medicine (IM) , Paediatrics (PED) , and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the CEO believes influences total charges per member per month is whether the doctor is a foreign or Australian medical school graduate. The CEO theorises that foreign graduates will have higher mean charges than Australian graduates. To investigate this, the CEO also collected data on 20 foreign medical school graduates in each of the four primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 Australian medical school graduates) was obtained for each of the four specialties. The results for the ANOVA are summarised in the following table.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Source } &{ d f } & { \text { S5 } } &{ \text { MS } } & { F } & { \text { PR } > \mathrm { F } } \\\hline \text { Specialty } & 3 & 22.855 & 7.618 & 60.94 & 0.0001 \\\hline \text { Med school } & 1 & 105 & 105 & 0.84 & 0.6744 \\\hline \text { Interaction } & 3 & 850 & 297 & 2.38 & 0.1348 \\\hline \text { Error } & 152 & 18,950 & & & \\\hline \text { Total } & 159 & 42,800 & & & \\\hline\end{array}$$
-Referring to Instruction 11-10,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 Australian medical school graduates?

• A) numerator df = 3, denominator df = 152
• B) numerator df = 1, denominator df = 152
• C) numerator df = 3, denominator df = 159
• D) numerator df = 1, denominator df = 159

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Definitions:

Feedback Loop

A system where the outputs loop back as inputs, influencing the process and potentially leading to self-amplifying or self-dampening outcomes.

Junk Science

Information or analysis claimed to be scientific but lacking in integrity, rigor, or adherence to established standards and methods.

Phase Change

A transition among the basic states of matter: solid, liquid, and gas, involving energy changes without altering the chemical composition of a substance.

Half-life

The time required for half the amount of a particular substance, such as a radioactive element or drug, to undergo a process of decay or elimination.