The operations manager for an appliance manufacturer wants to determine the optimal length of time for the washing cycle of a household clothes washer. An experiment is designed to measure the effect of detergent brand and washing cycle time on the amount of dirt removed from standard household laundry loads. Four brands of detergent (A.B,C,D) and four levels of washing cycles (18, 20, 22, and 24 minutes) are specifically selected for analysis. 32 standard household laundry loads (having equal weight and dirt) are randomly assigned to the 16 detergent-washing cycle time combinations. The results (in pounds of dirt removed) are: Washing Cycle Time (in Minutes) Brand 18 20 22 24 A 0.11 0.13 0.17 0.17 0.09 0.13 0.19 0.18 B 0.12 0.14 0.17 0.19 0.1 0.15 0.18 0.17 0.08 0.16 0.18 0.2 0.09 0.13 0.17 0.16 D 0.11 0.12 0.16 0.15 0.13 0.13 0.17 0.17 Perform a Two-way Analysis of Variance with Replication in Excel and output the ANOVA table assuming a 5% level of significance. Is there an effect due to washing cycle times? Why or why not? Support your answer by using the pvalue. O No, there is not an effect due to washing cycle time, pvalue = 0.519244 so the Null Hypothesis is not rejected. O Yes, there is not an effect due to washing cycle time, pvalue = 0.519244 so the Null Hypothesis is rejected. O No, there is not an effect due to washing cycle time, pvalue = 0.0000000178 so the Null Hypothesis is not rejected. O Yes, there is an effect due to washing cycle time, pvalue = 0.0000000178 so the Null Hypothesis is rejected.

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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Transcribed Image Text:The operations manager for an appliance manufacturer wants to determine the optimal length of time for the washing cycle of a household clothes washer. An experiment is designed to measure the effect of detergent brand and washing cycle time on the amount of dirt removed from standard household laundry loads. Four brands of detergent (A,B,C,D) and four levels of washing cycles (18, 20, 22, and 24 minutes) are specifically selected for analysis. 32 standard household laundry loads (having equal weight and dirt) are randomly assigned to the 16 detergent-washing cycle time combinations. The results (in pounds of dirt removed) are: Washing Cycle Time (in Minutes) Brand 18 20 22 24 A 0.11 0.13 0.17 0.17 0.09 0.13 0.19 0.18 B 0.12 0.14 0.17 0.19 0.1 0.15 0.18 0.17 0.08 0.16 0.18 0.2 0.09 0.13 0.17 0.16 D 0.11 0.12 0.16 0.15 0.13 0.13 0.17 0.17 Perform a Two-way Analysis of Variance with Replication in Excel and output the ANOVA table assuming a 5% level of significance. Is there an effect due to washing cycle times? Why or why not? Support your answer by using the pvalue. O No, there is not an effect due to washing cycle time, pvalue = 0.519244 so the Null Hypothesis is not rejected. O Yes, there is not an effect due to washing cycle time, pvalue = 0.519244 so the Null Hypothesis is rejected. O No, there is not an effect due to washing cycle time, pvalue = 0.0000000178 so the Null Hypothesis is not rejected. O Yes, there is an effect due to washing cycle time, pvalue = 0.0000000178 so the Null Hypothesis is rejected.

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