Robert Altoff is vice president for engineering for a manufacturer of household

Question

Robert Altoff is vice president for engineering for a manufacturer of household washing machines. As part of new product development, he wishes to determine the optimal length of time for the washing cycle. A part of the development is to study 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 below.

Complete an ANOVA table. Use the .05 significance level. (Round SS, MS, p to 3 decimal places and F to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

Robert Altoff is vice president for engineering for a manufacturer of household washing machines. As part of new product development, he wishes to determine the optimal length of time for the washing cycle. A part of the development is to study 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 below.

Explanation / Answer

Here the data is two way classified with respect to two factors as, "Detergent Brand" and "Cycle Time" , each having 4 levels.

Now the ANOVA Table is given below,

Source                             df                   SS                    MS                           F-ratio               p-value

Cycle                               3             0.023259            0.007753                      17.35                2.77 x 10-5

Detergent                       3              0.00504             0.001678                       3.755               0.0324

Interaction                     9              0.004103           0.000456                       1.020               0.4646

Error                               16            0.007150           0.000447                          --                      --

Total                               31             0.039546              --                                  --                      --

On the basis of the Table

we cannot reject

H01: There is no interaction effect between detergent - cycle time combiantions VS

H11: There is so ,

as pvalue = 0.4646 >> 0.05 .

So, on the basis of data there is no significant interaction between tdeterent brands and cycle times mentioned.

Then we proceed to test,

H02 : All the cycles have same amount of power to remove the dirt   VS

H12 : not H02 at 5% level as p-value = 2.77 x 10-5 << 0.05 .

So we conclude that there is significantly differential effect of various cycle times on amount of dirt cleansed.

Also ,

H03: All the degergent brand have same ability to remove the dirt VS

H13: Not H03 . at 5 % level we see p-value = 0.0324 < 0.05 , so, we reject H03 on the basis of the data and conclude that there is significantly different effect of the various detergent brands .

Cycle times                  Means

18 mins                       0.12625

20 mins                       0.13750

22 mins                        0.17500

24 mins                       0.19250

Brand            Mean

A                   0.16125

B                   0.15750

C                   0.17375

D    0.13875

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