Question

QUESTION 8 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) 20 24 0.17 0.18 0.19 Brand 0.11 0.09 0.12 0.1 0.08 009 0.11 0.13 0.17 0.19 0.17 0.18 0.18 0.17 0.16 0.17 0.13 0.14 0.15 0.16 0.13 0.12 0.13 0.2 0.16 0.15 0.17 Perform a Two-way Analysis of Variance with Replication in Excel and output the ANOVA table assuming a 5% level of significance. To answer the question, is there an effect due to detergent brand, what is the p-value? Round your answer to 2 decimal places

Answer 1

To test the following null hypothesis:

H₀: The means of observations grouped by 'Brand' are the same.

Vs Alternative hypotheses,

H_a: The means of observations grouped by 'Brand' are different.

Using excel,

Once the data is entered,

Here, rows per sample is the no. of observations in each group, i.e., the no .of observations of a Brand at one level of Washing Cycle Time is 2.

The output is obtained as follows:

Looking into the two way ANOVA table,

For the factor Brands (Sample),

No. of brands(n) = 4 and its corresponding df = n-1 = 3.

Here, the F statistic value is less than the tabled value.And the p value obtained is 0.519 >0.05.Therefore, we do not have sufficient evidence to reject H_0.We may accept H₀ at 5% level of significance.

It may be concluded that, the means of observations grouped by 'Brand' are the same.

Hence,

The p value for effect due to detergent brand is 0.52.Since it is not significant at 5% level, it may be concluded that there is no significant effect due to detergent brand.