Name___________________________________
ID______________________________________
STATISTICS (V31. 0018.009)
New York University
Inst. Luis J. Hall
Spring 2006
THE EXAM CONTAINS FOUR QUESTIONS.
PLEASE MAKE SURE TO ANSWER ALL OF THEM
Solve the problem.
All question in the problem has the same number of points.
1) (30 points) 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 costeffective than others. One theory is that Certification
Level is an important factor in measuring the costeffectiveness 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
a
= 0.01
Source
df
SS
Treatments
2
5422.968
Error
57
7455.6
a.
Explain the assumptions required for this ANOVA experiment.
b.
Determine the total variation in the sample and interpret the meaning of this total variation in the sample.
Explaing what is the meaning of an analysis of variance in this case?
c.
Is this a one or two factor experiment?
Explain.
d.
Write the null hypothesis tested by the ANOVA and the alternative hypothesis.
e.
Conduct an F test with 99% of confidence.
f.
Suppose that the researcher finds out after presenting his results that doctors can have both status when they
are Uncertified.
They can be eligible and ineligible at the same time and 10 doctors in the sample are appearing
in both groups.
Can this affect your previous result?
How would you fix this problem if it exists.
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 Summer '08
 Hall
 Regression Analysis, Null hypothesis, Statistical hypothesis testing, HMO, total variation

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