In September 1996, U.S. News & World Report published a report on America's health maintenance organizations (HMOs). The report was intended to serve as a consumer guide to HMO quality. For each HMO included in the report, data were provided on several variables, including the following:
PHYSTURN: Physician turnover rate (%).
PHYSCERT: Percentage of doctors who were board certified.
PREV: Prevention score, indicating how well the HMO meets Public Health Service goals in various measures of preventive care (including immunizations and prenatal care). The results can be negative (indicating that the HMO falls short of the goals) or positive (indicating that it exceeds the goals).

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a. In the U.S. News & World Report story, the average physician turnover rate for HMOs is reported to be 6%. Suppose that an ANOVA is to be performed to compare the average prevention scores for HMOs with low physician turnover rates (‰¤6%) and HMOs with higher rates (>6%). State precisely the ANOVA model.
b. In the above SAS output, complete the ANOVA table. To produce the output, the following coding scheme was followed: TURN = 1 if PHYSTURN ‰¤ 6%; 2 otherwise.
c. Test whether the average prevention scores differ significantly for the two types of HMOs mentioned in part (a).
d. Suppose that an ANOVA is to be performed to compare the average prevention scores for HMOs with low percentages of board-certified primary care physicians (‰¤75%) and HMOs with higher percentages of board-certified physicians (>75%). State precisely the ANOVA model.
e. In the second part of the above SAS output, complete the ANOVA table. To produce the output, the following coding scheme was followed: CERT = 1 if PHYSCERT ‰¤ 75%; 2 otherwise.
f. Test whether the average prevention scores differ significantly for the two types of HMOs mentioned in part (d).

PREV PHYSCERT Kaiser Foundation (HI Region) CIGNA HealthCare of LA CIGNA HealthCare of S. California CIGNA HealthCare of N. California HIP Health Plan of Florida CIGNA HealthCare of San Diego NYLCare of the Mid- Atlantic Personalcare Insurance of Illinois 21 13 CIGNA HealthCare of S. Florida Health Alliance Medical Plans Partners National Health. NC Healthsource of New Hampshire CLASS LEVEL INFORMATION Class Levels Values TURN 1 2 Number of Observations Road 18 Number of Observations Used 18 Dependent Variable: PREV DF Sum of Squares Mean Square F Value Pr> F Source Model Error Corrected Total 2868.56752 2868.56752 1.72 02085 6 26717 87692 17 29586 44444 1669 86731 R-Square Coeff Var Root MSE PREV Mean 0.096955 -154.5278 40.86401 26.44444 Source DF Type I SS Mean Square F Value Pr>F TURN 2868.587521 2868.567521 1.72 0.2085 Source F Type III SS Mean Square F ValuePr F TURN 2868.567521 2868.567521 1.72 02085 CLASS LEVEL INFORMATION Class Lovels Values BORDCERT 2 1 2 Number of Observations Read 18 Number of Observations Used 18 Dependent Variable: PREV DF Sum of Squares Mean Square FValue Pr> F 5.82 0.0306 Source Model Error Correctod Total 7691 37778 16 21895.08667 17 29586.44444 Coeff VarR 7691.37778 1368.44167 R-Square Root MSE PREV Mean 0.259963 -139.8874 36.99245 26.44444 DF Type I SSMean Square F Value Pr> F Source BORDCERT Source BORDCERT 7691.377778 7691 37777 562 0.0306 DF Type III SS Mean Square F Value Pr> 7091377778 7691.377778 562 0.0306