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The Accompanying Data Table Gives Observations on Total Acidity of Coal

question 18

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  Morwell  Yalloum  Maddingley .404 N8.27,8.178.66,8.618.14,7.96 NaOH Conc. .626 N8.03,8.218.42,8.588.02,7.89.786 N8.60,8.208.61,8.768.13,8.07\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, ijkxjjk2=1240.1525 and ijXij2=2479.9991\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.

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Definitions:

Heuristic

A problem-solving strategy that uses a practical method or various shortcuts to produce solutions that may not be optimal but are sufficient for immediate goals.

Mirror Test

A behavioral technique developed to assess self-awareness and the ability to recognize oneself in a mirror.

Self-awareness

The conscious knowledge of one's own character, feelings, motives, and desires.

Compensatory Model

In decision-making, this model suggests that individuals assess multiple aspects or attributes, compensating for weaker aspects with stronger ones.

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