23. The accompanying data was obtained in an experiment to investigate whether compressive strength of concrete cylinders depends on the type of capping material used or variability in different batches (“The Effect of Type of Capping Material on the Compressive Strength of Concrete Cylinders,” Proceedings ASTM, 1958: 1166–1186). Each number is a cell total (xij

) based on K
3 observations.

Batch 12 3 45 1 1847 1942 1935 1891 1795 Capping Material 2 1779 1850 1795 1785 1626 3 1806 1892 1889 1891 1756 In addition,


x 2 ijk
16,815,853 and

x 2 ij

50,443,409.

Obtain the ANOVA table and then test at level .01 the hypotheses H0G versus HaG, H0A versus HaA, and H0B versus HaB, assuming that capping is a fixed effect and batches is a random effect.