The article Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems (I. Sabuncuoglu, M. Fadiloglu, and S. C elik, IIE Transactions, 2008:538551) describes a

The article €œVariance Reduction Techniques: Experimental Comparison and Analysis for Single Systems€ (I. Sabuncuoglu, M. Fadiloglu, and S. C¸ elik, IIE Transactions, 2008:538€“551) describes a study of methods for reducing variance in estimators of the mean inventory on hand. Two systems, the serial line system and the inventory system, were studied, along with two schemes for proportional sampling. The results given below (in percent) are consistent with the means and standard deviations reported in the article.

a. Estimate all main effects and interactions.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Is the additive model plausible? Provide the value of a test statistic and the P-value.

d. Can the effect of system on reduction be described by interpreting the main effects of system? If so, interpret the main effects, including the appropriate test statistic and P-value. If not, explain why not.

e. Can the effect of scheme on reduction be described by interpreting the main effects of scheme? If so, interpret the main effects, including the appropriate test statistic and P-value. If not, explain why not.

System Scheme Reduction Serial Line A 6.4 5.8 5.1 8.4 7.0 8.4 8.5 7.5 7.0 7.9 Serial Line B 4.7 4.7 3.8 5.3 10.6 4.5 8.2 10.8 5.1 5.7 12.5 Inventory Inventory A 11.0 8.9 9.3 9.2 7.9 9.7 9.0 6.7 9.8 B 8.9 7.0 10.7 10.3 6.2 12.2 7.0 9.5 8.7 9.7