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

question 147

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,interpret the test for interaction.

• A) There is sufficient evidence to say at the 0.10 level of significance that the difference between the mean charges for foreign and Australian graduates depends on primary specialty.
• B) There is sufficient evidence at the 0.10 level of significance of a difference between the mean charges for foreign and Australian medical graduates.
• C) There is sufficient evidence to say at the 0.10 level of significance that mean charges depend on both primary specialty and medical school.
• D) There is insufficient evidence to say at the 0.10 level of significance that the difference between the mean charges for foreign and Australian graduates depends on primary specialty.

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Definitions:

Bins

Categories or intervals used in data analysis to group data points for easier analysis, especially in histograms.

Acres

A unit of area, primarily used in the United States, equal to 43,560 square feet or approximately 4,047 square meters.

Stem-and-Leaf Display

A graphical method of displaying numerical data, where each number is divided into a stem (the leading digit(s)) and a leaf (the last digit).

Kilograms

A unit of mass in the International System of Units (SI), equal to one thousand grams or approximately 2.20462 pounds.