To examine whether mathematics skills of the average high school graduate in urban areas of the United States have declined over the past 10 years, the average scores on the math section of the SAT Reasoning Test (MSAT) were compared for a random sample of five big-city high schools for the years 2002, 2007, and 2012. The results are shown in the following table and accompanying computer output.

a. Determine the sample means for each year.
b. Comment on the independence assumption required for using one-way ANOVA on the data given.
c. Determine the one-way ANOVA table for these data.
d. Test by means of a one-way ANOVA whether any significant differences exist among the three MSAT average scores for the years 2002, 2007, and 2012.
e. Use Scheffe's method to locate any significant differences between pairs of means. (Use α = .05.)

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Year School 1 School 2 School 3 School 4 School 5 2002 2007 2012 550 545 536 535 528 526 532 527 541 530 552 Dependent Variable: vsat OF Sum of Squares Mean Square F Value Pr> F Source Model Error Corrected Total 548.133333 1453.600000 2001.733333 274.066667 2.26 0.1466 12 121.133333 14 R-Square Coeff Var Root MSE vsat Mean 0.273829 2.032638 11 11.00606 541.4667 Source DF Type I SS Mean Square F Value Pr> F 2 548.1333333 274.0666667 2.26 0.1466 year Source DF Type III SS Mean SquareF Value Pr> F year 548.1333333 274.0666667 2.26 0.1466