Problem 13.7 The data below come from a larger experiment to determine the effective[1]ness of blast furnace slags (A) as agricultural liming materials on three types of soil (B): sandy loam (1), sandy clay loam (2), and loamy sand (3). The treatments were all applied at 4000 lbs per acre and the response variable was the corn yield in bushels per acre.

(a) Calculate the ANOVA table and use your results to test for differences among the treat[1]ment means. Use α = 0.05.

(b) Plot the residuals against the fitted values. Do you see any non-random patterns?

(c) Calculate the normal probability plot of the residuals and test the residuals for normality using the Shapiro–Wilk test.

(d) Plot (i, yij )(i = 1,..., 7) for each soil type; follow the pattern used to obtain Figure 13.2. Does the graph support or refute the assumption that there are no treatment–block interactions?

Soil (B) Furnace slags (A) 123 None 11.1 32.6 63.3 Coarse slag 15.3 40.8 65.0 Medium slag 22.7 52.1 58.8 Agricultural slag 23.8 52.8 61.4 Agricultural limestone 25.6 63.1 41.1 Agricultural slag + minor elements 31.2 59.5 78.1 Agricultural limestone + minor elements 25.8 55.3 60.2