QUESTION9 The operations manager for an appliance manufacturer wants to determin

Question

QUESTION9 The operations manager for an appliance manufacturer wants to determine the optimal length of time for the washing cycle of a houschold 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 CD) 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 20 0.13 0.13 0.14 0.15 0.16 0.13 0.12 0.13 24 0.17 0.18 0.19 0.11 0.09 0.19 0.08 0.09 0.11 0.13 0.18 0.18 0.17 0.16 0.2 0.16 0.15 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. No, there is not an effect due to washing cycle time, pvalue 0519244 so the Null Hypothesis is not rejected. Yes, there is not an effect due to washing cycle time, pvalue-0.519244 so the Null Hypothesis is rejected No, there is not an effect due to washing cycle time, pvalue 00000000178 so the Null Hypothesis is not rejected. Yes, there is an effect due to washing cycle time, pvalue-00000000178 so the Null Hypothesis is rejected.

Explanation / Answer

here applying two way ANOVA on abvoe data:

correct option is : Yes there is an effect due to washing cycle time; p value =0.0000000178 o the null hypothesis is rejected.

Source of Variation SS df MS F P-value F crit Brand 0.000413 3 0.000138 0.785714 0.5192444602 3.238872 washing cycle time 0.027338 3 0.009113 52.07143 0.0000000178 3.238872 Interaction 0.002337 9 0.00026 1.484127 0.2351179537 2.537667 Within 0.0028 16 0.000175 Total 0.032888 31

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