The data shown in the table below are the results of an experiment conducted to investigate the effect of three factors on the percentage of ash in coal. 

The three factors, each at four levels, were 

Type of coal (factor A): Mojiri, Michel, Kairan, and Metallurgical coke 

Maximum particle size (factor B): 246, 147, 74, and 48 microns 

Weight of selected coal specimen (factor C): 1 gram, 100 milligrams, 20 milligrams, and 5 milligrams 

Three specimens were prepared for each of the 4 × 4 factor–level combinations, yielding three replications of a complete factorial experiment.
a. Set up an analysis of variance table showing the sources and degrees of freedom for each.

b. Do the data provide evidence of any interactions among the factors? Test using α = .05.

c. Does the mean level of coal ash obtained in the analysis depend on the weight of the coal specimen? Test using α = .05.

d. Find 95% confidence intervals for the difference in the mean ash content between Mojiri and Michel coal at each of the four levels of maximum particle size.

Transcribed Image Text:

COALASH A, Mojiri Az Michel Аз Kairan Ag Met. Coke sample Replication x1 X2 X3 X1 X2 X3 X1 X2 X3 X1 X2 X3 B, CI 7.30 7.35 7.42 10.69 10.58 10.72 12.20 12.27 12.23 9.99 10.02 9.95 C2 6.84 6.07 6.91 10.26 10.35 10.42 11.85 11.85 12.05 9.45 9.86 9.78 C3 7.05 6.49 7.24 10.61 10.08 10.31 12.34 11.74 11.44 9.76 9.79 9.77 C4 6.75 5.62 7.24 10.66 10.61 10.01 12.22 11.68 12.09 9.92 10.17 10.50 B2 CI 7.56 7.44 7.51 10.86 10.88 10.90 12.47 12.42 12.44 9.87 9.81 9.79 C2 7.10 7.37 7.32 10.45 10.62 10.87 12.47 12.28 12.04 9.46 9.60 9.62 C3 7.41 7.60 7.49 10.85 10.89 10.61 12.33 12.35 12.40 9.97 9.77 9.76 C4 7.29 7.62 7.43 10.68 11.58 10.60 12.04 12.21 12.51 9.76 10.10 9.61 B3 CI 7.51 7.64 7.58 10.30 10.68 10.73 12.42 12.41 12.39 9.97 10.02 10.01 C2 7.36 7.50 7.21 10.33 10.50 10.64 12.05 12.30 12.20 9.78 10.02 9.91 C3 7.56 7.55 7.47 10.73 10.75 10.84 12.44 12.30 12.26 9.88 9.90 10.06 C4 7.71 7.67 7.76 10.92 10.80 10.79 12.11 12.02 12.26 9.77 9.74 9.69 B4 CI 7.45 7.49 7.47 10.85 10.89 10.85 12.23 12.30 12.17 10.06 10.07 10.11 C2 7.15 7.68 7.18 10.37 10.79 10.71 11.52 12.17 11.82 9.71 9.86 9.78 C3 7.60 7.55 6.61 10.82 10.82 10.88 12.40 11.99 12.17 10.13 9.93 10.01 C4 8.06 7.05 7.57 11.26 10.56 10.31 11.96 11.87 12.06 10.01 9.98 9.84