6.20. Consider a variation of the bottle filling experiment from Example 5.3. Suppose that only two levels of carbonation are used so that the experiment is a 23 factorial design with two replicates. The data are shown in Table P6.3.

(a) Analyze the data from this experiment. Which factors significantly affect fill height deviation?

(b) Analyze the residuals from this experiment. Are there any indications of model inadequacy?

(c) Obtain a model for predicting fill height deviation in terms of the important process variables. Use this model to construct contour plots to assist in interpreting the results of the experiment.

(d) In part (a), you probably noticed that there was an interaction term that was borderline significant. If you did not include the interaction term in your model, include it now and repeat the analysis. What difference did this make? If you elected to include the interaction term in part (a), remove it and repeat the analysis. What difference does the interaction term make?

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Coded Factors Fill Height Deviation Factor Levels Run A B C Replicate 1 Replicate 2 Low (-1) High (+1) 1 -3 -1 A (%) 10 12 2 + 0 1 B (psi) 25 30 3 1 0 C (b/m) 200 250 4 819 5 6 +1+ 1+ 2 3 7 +1 ++ + ++ -1 0 2 1 + 6 1 1 5