A Certain HMO Is Attempting to Show the Benefits of Managed

question 27

Multiple Choice

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 were subjected to an analysis of variance. The results of the ANOVA are summarized in the following table. Take $\alpha$ $= 0.01$
$\begin{array}{lrcccc}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F Value } & \text { Prob }>\text { F } \\\hline \text { Treatments } & 2 & 4083.81 & 2041.905 & 20.73 & .0001 \\\text { Error } & 57 & 5614.5 & 98.5 & & \\\text { Total } & 59 & 9698.31 & & &\end{array}$

Interpret the $p$ -value of the ANOVA $F$ -test.

• A) The variances of the total per number per month charges for the three groups of physicians differ at \(\alpha = .01\).
• B) The means of the total per member per month charges for the three groups of physicians are equal at \(\alpha = .01\).
• C) The model is not statistically useful (at \(\alpha = .01\) ) for prediction purposes.
• D) The means of the total per member per month charges for the three groups of physicians differ at \(\alpha = .01\).

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Definitions:

Progressive Income Tax

A tax system in which the tax rate increases as the taxable income increases, aiming to distribute the tax burden more equitably.

Proportional Tax

A tax system where the rate of tax is constant regardless of the amount subject to tax, meaning everyone pays the same percentage of their income.

Local Tax

Taxes imposed by local government entities, such as cities or counties, typically used to fund local services like schools, roads, and public safety.

Business Property

Assets owned by a business, including physical property like real estate and equipment, as well as intangible assets like intellectual property.