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 В 0.12 0.14 0.17 0.19 0.1 0.15 0.18 0.17 0.08 0.16 0.18 0.2 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 a significant interaction between detergent brand and washing cycle time? Why or why not?
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 В 0.12 0.14 0.17 0.19 0.1 0.15 0.18 0.17 0.08 0.16 0.18 0.2 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 a significant interaction between detergent brand and washing cycle time? Why or why not?
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 a significant interaction between detergent brand and washing cycle time?
Why or why not?
O There is no interaction between detergent brand and washing cycle time since the pvalue(0.235118) is greater than the 5% level of significance.
O There is an interaction between detergent brand and washing cycle time since the pvalue (1.5E-09) is less than the 5% level of significance.
There is no interaction between detergent brand and washing cycle time since the F test statistic does not fall in the rejection region with an F-critical value of 2.99612.
There is an interaction between detergent brand and washing cycle time since the F test statistic falls in the rejection region with an F-critical value of 3.008787.
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