The Accompanying Data Table Gives Observations on Total Acidity of Coal

Essay

The accompanying data table gives observations on total acidity of coal samples of three different types, with determinations made using three different concentrations of ethanolic NaOH.
Type of Coal $$\begin{array} { c c | c c c } && { \text { Morwell } } & \text { Yalloum } & \text { Maddingley } \\\hline & .404 \mathrm {~N} & 8.27,8.17 & 8.66,8.61 & 8.14,7.96 \\\text { NaOH Conc. } & .626 \mathrm {~N} & 8.03,8.21 & 8.42,8.58 & 8.02,7.89 \\& .786 \mathrm {~N} & 8.60,8.20 & 8.61,8.76 & 8.13,8.07 \\& & & & \\\hline\end{array}$$ Additionally, $$\sum _ { i } \sum _ { j } \sum _ { k } x _ { j j k } ^ { 2 } = 1240.1525 \text { and } \sum _ { i } \sum _ { j } X_{ij\square} ^ { 2 } = 2479.9991$$
a. Assuming both effects to be fixed, construct an ANOVA table, test for the presence of
ANOVA table, test for the presence of interaction, and then test for the presence of main effects for each factor (all using level .01).
b. Use Tukey's procedure to identify significant differences among the types of coal.