Adding glass particles to clay brick may improve the structural properties of the brick. The article ??Effects of Waste Glass Additions on the Properties and Durability of Fired Clay Brick?? (S. Chidiac and L. Federico, Can J Civ Eng, 2007:1458??1466) describes experiments in which the compressive strength (in MPa) was measured for bricks with varying amounts of glass content and glass particle size. The results in the following table are consistent with means and standard deviations presented in the article.

a. Estimate all main effects and interactions.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Is the additive model plausible? Provide the value of a test statistic and the P-value.

d. Can the effect of glass content on strength be described by interpreting the main effects of glass content? If so, interpret the main effects, including the appropriate test statistic and P-value. If not, explain why not.

e. Can the effect of particle size on strength be described by interpreting the main effects of particle size? If so, interpret the main effects, including the appropriate test statistic and P-value. If not, explain why not.

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Glass Content (%) Size Strength (MPa) 78.7 73.0 5 Coarse 70.8 78.6 81.7 79.2 5 Fine 90.1 71.4 93.8 82.7 10 Coarse 80.1 76.9 77.7 76.5 121.2 84.3 81.4 10 Fine 76.2 80.1 61.2 15 Coarse 90.3 95.8 103.1 99.5 73.3 15 Fine 141.1 144.1 122.4 134.5 124.9