Problem Definition/Research Objective: The operations manager for a soft drink distributoris interested in obtaining a more uniform/consistent fill height in the bottles filled during the bottling process at the distributions center. Supposedly, available machinery fills each bottle to the correct level, but in practice, there is variation around the specified target.

Typically, 25 psi is desirable for the equipment on hand. Two additional variables may affect the variation associated with the filling process: percent carbonation (10% or 12%) and or line speed (either 210, 240, 270, or 300 bottles per minute).

Use Two ANOVA to determine if percent carbonation (Factor 1 and Line Speed Factor 2) have effect on variation in bottle fill.

The response variable is: Deviations/variation from specified target fill in millimeters.

Factor 1 is percent carbonation Factor 2 is Line Speed

Note: In this case higher mean deviation does not represent the optimal result. Deviation is the "miss" from the desired fill height.

Complete the following for the two-way ANOVA. The finished report should contain the following in the order specified:

Test Assumptions first

Use a six-step process to determine if the variances of the eight cell combinations of Line Speed and Carbonation on Bottle fill height are equal. Use p-values to test hypothesis of equal variances. Remember, there is one variance per cell (combination of per treatment of Percent Carbonation and Line Speed on Bottle Fill). *Hint: Eight cells require eight variances.

Use NP Plot to satisfy the assumption of normality. Recall residuals are plotted on the NP Plot e= x x. Each dot on the plot is a residual. Discuss graph as evidence of whether the assumption of normality is satisfied. See Page 11 of handout.

Using ANOVA to test the three hypotheses under two-way ANOVA: Problem Definition: Conduct Two Way ANOVA with interaction to test mean deviation in bottle fill.

In Minitab, make a two-way ANOVA formatted as a single six-step process. Show all three hypotheses under Hypothesis section and display the ANOVA one time in your report. Showing the ANOVA Minitab readout for each hypothesis will result in a 3-point deduction for each offense. Row Factor and Column Factor. Each requires six step process. Analyze the Minitab output appropriate testing sequence for two-way ANOVA to test the hypotheses. For the Conclusion, use both p values and critical value/critical ratio to all hypothesis tests. Remember to test the null of no interaction first. If FTR you must test the remaining hypotheses.

If appropriate, use Tukey pairwise comparisons to test significant factor levels. This is a six step so provide a problem definition: Be sure to format all hypothesis testing using the six-step process. Address results of Tukey test in regard to determining the best combination of row and column factor to produce most accurate bottle fill. Show the Tukey output and six step process in a separate section of your report and provide the Tukey testing only if required (rejected any of the hypotheses in the ANOVA.

Provide interactions plots and describe what you see in terms of rejected null hypothesis or hypotheses.