The data in the accompanying table were sampled from U.S. News & World Report's 1996 story on the "Best Mutual Funds." The following variables are shown for each fund:
CAT (fund category):
1 = Aggressive growth; 2 = Long-term growth; 3 = Growth and income; 4 = Income.
LOAD (load status):
N = No load; L = Load.
VOL (volatility):
A letter grade from A+ to F indicating how much the month-to-month return varied from the fund's three-year total return: A+ = Least variability; F = Most variability.
OPI (Overall Performance Index):
An overall measure of the relative performance of each fund over the past 1, 3, 5, and 10 years. The higher the OPI, the better the performance.

a. Suppose that an ANOVA is to be performed to compare the average OPI values for the different fund categories. State precisely the ANOVA model. Is fund category a fixed- or random-effects factor?
b. Using the SAS output that follows, complete the ANOVA table.
c. Test whether the average overall performance indices (OPI) differ significantly across the four fund categories (CAT).
d. Use the Tukey-Kramer method to locate any significant differences between pairs of means. (Use a = .05.)

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Fund CAT LOAD VOL OPI 20th Century Giftrust Investors AIM Aggressive Growth Stein Roe Capital Opportunity FPA Capital Third Avenue Valuc Phoenix U.S. Govt. A Vanguard Primecap MFS Research A Fidelity Valu Mairs&Power Growh Guardian Park Avenue AIM Valuc A Lexington Corp. Leaders Fundamental Investors Oppenheimer Main St. Inc & Growth A MAS Value Portfolio Vanguard Index Value Putnam Growth and Income Federated Liberty Equity Income A United Income A Benham Inc. & Growth Manager's Income Equity Pioneer Equity Income One Group Income Equity A 89.9 88.1 92.2 88.2 88.0 93.9 D+ 94.5 99.1 92.2 D+ 906 91.3 92.7 D+90.8 99.8 88.9 90.8 89.5 C+ 768 89.8 84.7 84.0 B+ 83.3 CLASS LEVEL INFORMATION Class Levels Values CAT 4 1234 Number of Observations Read 24 Number of Observations Used 24 Dependent Variable: OPI Source DF Sum of Squares Mean Square F Value Pr> F 282.0545833 255.5050000 23 5375595833 Model 94.0181944 20 12.7752500 Corrected Total R-Square Coeff VarRoot MSE 0.524695 OPI Mean 3 966062 3.574248 90.12083 Source DF Type I SS Mean Square FValue Pr> F GAT 282.0545833 94.0181944 7.36 0.0016 Source DF Type Ill ss CAT Mean Square F Value Pr F 282 0545833 94,0181944 7.38 0.0016 Tukey's Studentized Range (HSD) Test for OPI Alpha Error Degrees of Freedom Error Mean Square Critical Value of Studentized Range Minimum Significant Difference 0.05 20 2.77525 3.95825 5.7758 MEANS WITH THE SAME LETTER ARE NOT SIGNIFICANTLY DIFFERENT Tukey Grouping MeanN CAT A 93617 62 A 92.383 6 A 89.800 6 84.683 6