Question

can someone please check my answer, thanks!

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 0.11 0.13 0.17 0.17 0.09 0.13 0.19 0.18 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. Which washing cycle times do NOT show a significant different results (at alpha = 0.05) in the pounds of dirt removed? Perform the multiple comparisons procedure, Fisher's LSD, by hand to determine the result. Select all answers that apply. 18 and 20 minutes 18 and 22 minutes 18 and 24 minutes 20 and 22 minutes 20 and 24 minutes 22 and 24 minutes

Answer 1

Anova: Two-Factor With Replication
SUMMARY	18	20	22	24	Total
A
Count	2	2	2	2	8
Sum	0.2	0.26	0.36	0.35	1.17
Average	0.1	0.13	0.18	0.175	0.14625
Variance	0.0002	0	0.0002	5E-05	0.001313
B
Count	2	2	2	2	8
Sum	0.22	0.29	0.35	0.36	1.22
Average	0.11	0.145	0.175	0.18	0.1525
Variance	0.0002	5E-05	5E-05	0.0002	0.000964
C
Count	2	2	2	2	8
Sum	0.17	0.29	0.35	0.36	1.17
Average	0.085	0.145	0.175	0.18	0.14625
Variance	0.00005	0.00045	5E-05	0.0008	0.001827
D
Count	2	2	2	2	8
Sum	0.24	0.25	0.33	0.32	1.14
Average	0.12	0.125	0.165	0.16	0.1425
Variance	0.0002	5E-05	5E-05	0.0002	0.000536
Total
Count	8	8	8	8
Sum	0.83	1.09	1.39	1.39
Average	0.10375	0.13625	0.17375	0.17375
Variance	0.000284	0.00017	8.39E-05	0.000255
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0.000413	3	0.000138	0.785714	0.519244	3.238872
Columns	0.027338	3	0.009113	52.07143	1.78E-08	3.238872
Interaction	0.002337	9	0.00026	1.484127	0.235118	2.537667
Within	0.0028	16	0.000175
Total	0.032888	31

===============

Level of significance=	0.0500
no. of treatments,k=	4
DF error =N-k=	16
MSE=	0.000175
t-critical value,t(α/2,df)=	2.1199

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj)) = 0.01
if absolute difference of means > critical value,means are significnantly different ,otherwise not

SUMMARY	18	20	22	24
Count	8	8	8	8
Sum	0.83	1.09	1.39	1.39
Average	0.10375	0.13625	0.17375	0.17375

population mean difference		critical value			result
µ1-µ2	0.033	0.01			means are different
µ1-µ3	0.070	0.01			means are different
µ1-µ4	0.070	0.01			means are different
µ2-µ3	0.038	0.01			means are different
µ2-µ4	0.038	0.01			means are different
µ3-µ4	0.000	0.01			means are not different

answer:

18 and 20 minutes 18 and 22 minutes 18 and 24 minutes 20 and 22 minutes 20 and 24 minutes

Answer 2

i agree with the explanation of the comment above but the question says the word NOT so maybe it's only 22 and 24 minutes