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48. FILE Robert Altoff is vice president of engineering for a manufacturer of household washing machines. As part of a new product development project, he wishes to determine the optimal length of time for the washing cycle. Included in the project is a study of the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent-washing cycle combinations. The results (in pounds of dirt removed) are shown here: Detergent Brand A B с D Cycle Time (min) 18 20 22 24 0.13 0.12 0.19 0.15 0.11 0.11 0.17 0.18 0.14 0.15 0.18 0.20 0.10 0.14 0.17 0.18 0.16 0.15 0.18 0.19 0.17 0.14 0.19 0.21 0.09 0.12 0.16 0.15 0.13 0.13 0.16 0.17 a. Draw an interaction plot of the detergent means by cycle time. b. Compute the ANOVA with statistical software and, using the .05 significance level, test the interaction effect of brand and cycle time on "dirt removed." c. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means. d. Interpret the results in a brief report.

48. FILE Robert Altoff is vice president of engineering for a manufacturer of household washing machines. As part of a new product development project, he wishes to determine the optimal length of time for the washing cycle. Included in the project is a study of the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent-washing cycle combinations. The results (in pounds of dirt removed) are shown here: Detergent Brand A B с D Cycle Time (min) 18 20 22 24 0.13 0.12 0.19 0.15 0.11 0.11 0.17 0.18 0.14 0.15 0.18 0.20 0.10 0.14 0.17 0.18 0.16 0.15 0.18 0.19 0.17 0.14 0.19 0.21 0.09 0.12 0.16 0.15 0.13 0.13 0.16 0.17 a. Draw an interaction plot of the detergent means by cycle time. b. Compute the ANOVA with statistical software and, using the .05 significance level, test the interaction effect of brand and cycle time on "dirt removed." c. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means. d. Interpret the results in a brief report.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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48. FILE Robert Altoff is vice president of engineering for a manufacturer of household washing machines. As part of a new product development project, he wishes to determine the optimal length of time for the washing cycle. Included in the project is a study of the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent-washing cycle combinations. The results (in pounds of dirt removed) are shown here: Detergent Brand A B с D Cycle Time (min) 18 20 22 24 0.13 0.12 0.19 0.15 0.11 0.11 0.17 0.18 0.14 0.15 0.18 0.20 0.10 0.14 0.17 0.18 0.16 0.15 0.18 0.19 0.17 0.14 0.19 0.21 0.09 0.12 0.16 0.15 0.13 0.13 0.16 0.17 a. Draw an interaction plot of the detergent means by cycle time. b. Compute the ANOVA with statistical software and, using the .05 significance level, test the interaction effect of brand and cycle time on "dirt removed." c. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means. d. Interpret the results in a brief report.
Transcribed Image Text:48. FILE Robert Altoff is vice president of engineering for a manufacturer of household washing machines. As part of a new product development project, he wishes to determine the optimal length of time for the washing cycle. Included in the project is a study of the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent-washing cycle combinations. The results (in pounds of dirt removed) are shown here: Detergent Brand A B с D Cycle Time (min) 18 20 22 24 0.13 0.12 0.19 0.15 0.11 0.11 0.17 0.18 0.14 0.15 0.18 0.20 0.10 0.14 0.17 0.18 0.16 0.15 0.18 0.19 0.17 0.14 0.19 0.21 0.09 0.12 0.16 0.15 0.13 0.13 0.16 0.17 a. Draw an interaction plot of the detergent means by cycle time. b. Compute the ANOVA with statistical software and, using the .05 significance level, test the interaction effect of brand and cycle time on "dirt removed." c. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means. d. Interpret the results in a brief report.
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