Data on law and business schools were sampled from U.S. News & World Report's 1996 report on the "America's Best Graduate Schools 1996 Annual Guide." The school's reputation rank among academics and the 1995 median starting salary for graduates are shown in the accompanying table for 12 randomly sampled law schools and 12 randomly sampled business schools.

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a. Suppose that an ANOVA is to be performed to compare the average 1995 starting salaries (SAL) for business and law schools (let the variable SCHOOL = Law or Business, depending on the type of school). State precisely the ANOVA model. Is SCHOOL a fixed- or random-effects factor?
b. In the above SAS output, complete the ANOVA table.
c. Test whether the average 1995 starting salaries differ significantly for graduates of law schools and of business schools.
d. Suppose that an ANOVA is to be performed to compare the average 1995 starting salaries (SAL) for the top 25 schools and schools not in the top 25 in terms of reputation rank (let the variable REP = 1 if a school's reputation rank is 25 or less, REP = 2 if the rank is 26 or more). State precisely the ANOVA model.
e. In the second part of the above SAS output, complete the ANOVA table.
f. Test whether the average 1995 starting salaries differ significantly between top 25 schools and schools not in the top 25 in terms of reputation rank.

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Reputation Rank by Academics 1995 Median Starting Salaries (in $1000s) University School Vanderbilt University University of Chicago Brigham Young University George Washington University Cornell University Rurgers University University of Pennsylvania University of Ilinois (Urbana-Champaign) Villanova University University of Florida Tulane University Case Western Reserve University University of Georgia Tulane University University of Southern California Brigham Young University Emory University University of Illinois (Urbana- Champaign) Cornell University University of North Carolina (Chapel Hill Massichusetts Institute of Technology University of Texas (Austin) College of William and Mary Penn State University Law 45.5 24 Law 70 62 Law Law 43.4 Law Business Business Business Business Business Business Business Business Business Business 24 24 10 59 75 19 48 7 Business CLASS LEVEL INFORMATION Levels Values SCHOOL 2 Bus Law Number of Observations Read 24 Number of Observations Used 24 Dependent Variable: SAL DF Sum of Squares Mean Square F Value Pr> F Source Model Error Corrected Total 37.001667 22 1929.391667 23 1966 393333 37.001687 87 699621 R-Square Coeff Var Root MSE SAL Mean 0.018817 16.44873 9.364808 56.93333 Type I SS Source SCHOOL Source SCHOOL DF Mean Square F Value Pr> F 37.00166867 37.00166667 0.42 0.5227 DF Type IlI SS Mean Square F Value Pr> F 37.00166667 37.00166667 0.42 0.5227 CLASS LEVEL INFORMATION Class Levels Values REP 1 2 Number of Observations Read 24 Number of Observations Used 24 Dependent Variable: SAL DF Sum of Squares Mean Square FValue Pr>F Source Model Error Corrected Total 440.326667 69.386667 440.326667 22 1526.066667 23 1966.393333 R-Square Coeff VarRoot MSE SAL Mean 0.223926 14.62880 8.328665 56.93333 SourceDFType lSs Mean Square F Value Pr> F REP 1 440 3266667 440.3266667 6.35 0.0195 Source DF Type III SS Mean Square F Value Pr>F REP 440 3266667 440.3266667 6.35 0.0195