Question

...l Verizon 21:37 6% Х MBA 626 Case Stu... Q MBA 626 Case Study Two-Way ANOVA Product development engineers and marketers at a household washing machine manufacturing firm want to determine the optimal length of time for a washing cycle. Part of the study includes understanding 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 amount 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. (Note: The higher the number, the more dirt removed). Detergent Brand А B Cycle Time (in min) 18 20 0.13 0.12 0.11 0.11 0.14 0.15 0.10 0.14 0.16 0.15 0.17 0.14 0.09 0.12 0.13 0.13 22 0.19 0.17 0.18 0.17 0.18 0.19 0.16 0.16 24 0.15 0.18 0.20 0.18 0.19 0.21 0.15 0.17 с D a) Draw an interaction plot of the detergent means by cycle time. b) Compute the ANOVA using Excel and using the 0.05 significance level, test the interaction effect of brand and cycle time on "dirt removed." c) Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means. d) Write a 1-2 page paper, using APA format, explaining how you interpret the results of this study. Please see the attached rubric "RUBRIC MBA SLO 1.2 MBA 626 Case Study for these details which will be used for grading purposes. e) Upload to the designated ECN Assignment tab by the due date/time. Edit in Google Docs

Answer 1

(a) The plots are:

Interaction Plot by Factor 1 0.250 0.200 B 0.150 + Cell Mean 0.100 0.050 0.000 A B с - 18 min 20 min 22 min 24 min

Interaction Plot by Factor 2 0.250 0.200 0.150 + Cell Mean 0.100 0.050 0.000 18 min 20 min 22 min 24 min A B C D

(b)

Source	SS	df	MS	F	p-value
Factor 1	0.0057	3	0.00191	8.98	.0010
Factor 2	0.0172	3	0.00574	27.02	1.68E-06
Interaction	0.0022	9	0.00024	1.15	.3860
Error	0.0034	16	0.00021
Total	0.0286	31

(c) The hypothesis being tested is:

H₀: There is no main effect of Detergent Brand

H_a: There is a main effect of Detergent Brand

The p-value is 0.0010.

Since the p-value (0.0010) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of Detergent Brand.

The hypothesis being tested is:

H₀: There is no main effect of Cycle Time

H_a: There is a main effect of Cycle Time

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of Cycle Time.

The hypothesis being tested is:

H₀: There is no interaction effect

H_a: There is an interaction effect

The p-value is 0.3860.

Since the p-value (0.3860) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that here is an interaction effect.

(d) There is a main effect of Detergent Brand. (F (3, 16) = 8.98, p < 0.05)

There is a main effect of Detergent Brand. (F (3, 16) = 27.02, p < 0.05)

There is no interaction effect. (F (9, 16) = 1.15, p > 0.05)

Detergent Brand	18 min	20 min	22 min	24 min
A	0.13	0.12	0.19	0.15
	0.11	0.11	0.17	0.18
B	0.14	0.15	0.18	0.2
	0.1	0.14	0.17	0.18
C	0.16	0.15	0.18	0.19
	0.17	0.14	0.19	0.21
D	0.09	0.12	0.16	0.15
	0.13	0.13	0.16	0.17