An experiment was conducted to detemine whether either firin

An experiment was conducted to detemine whether either firing temperature or fumace position each at two levels, affects the baked density of carbon anode. Three replicates of this design are run. Below a partially completed estimate table and ANOVAtable for the experiment. Effect Coef SE Coef Term 0.000 Constant 793.1 505 176.05 Pos 48.33 24.17 5.36 Temp 481.67 240.83 0.000 Post Temp 7.67 3.83 4.505 Analysis of Variance for Density (coded units) MS F P Source DF SS 0.001 Pos 7008 28.77 Temp 696008 176 176 10.72 Pos Temp Residual error 1949 705142 a. Calculate all the missing values in the ANOVA table b. Write the appropriate hypothesis and use this table to test for the significance of the effects. Use 30.05 c. Find all the missing values in the estimate table. Indicate which effects are significant. Use a 0.05 d. Write the least squares fitted model using only the significant effects. e. Use the model to predict the response when x: -1, 1. f Use the means table below to construct the interaction plot. Does the plot agree with your results on (c), why? Temp 572 61. 1062 532 1006 g. Compute an approximate 95% CI for each effect. Compare your results with those in c).

Solution

a.

The value of SE Coef for POS is -48.33/-24.17 = 1.9996.

The value of SE Coef for Temp is 481.67/240.83 = 2.0000.

Answer for ANOVA table in color.

The Pos and Temp are at 2 levels with three replicates each. Hence, the degrees of freedom respectively for Pos, Temp, Pos*Temp, Residual error, and Total are respectively (2 -1) = 1, (2-1) = 1, (2-1)(2-1) = 1, 2 2 (3-1) = 8, and 2 2 3 -1 = 11 degrees of freedom.

The value of MS for Pos, Temp and Residual are hence, 7008/1 = 7008, 696008/1 = 696008, and 1949/8 = 243.625 respectively.

The F statistic value for Temp is 696008/243.625 = 2856.883.

The p-value for Temp is 0, which is value of F-statistic in the previous step.

b. The 0.05 level of significance, the Pos and Temp have significant impact while the interaction effect is insignificant.

c. The main effects are significant while the interaction is not at 0.05 level of significance.