Work #36. In the blue book this is on page 32. Give the calculated F for the det
ID: 3048791 • Letter: W
Question
Work #36. In the blue book this is on page 32. Give the calculated F for the detergent brand, for the washing time and for the interaction effect. Answer questions a, b, c, d, e, f.
When giving the calculated F don't just refer to F in the ANOVA table. State F for detergents; F for washing times and F for interaction. For questions a, b, c, please answer "Yes" or "No" and explain why you answered yes or no. Also answer them in order: put a) and your answer; put b) and your answer; put c) and your answer. Otherwise you won't get credit for a, b, c. Also please note that if the p value comes out to be 1.78E-08 that means 1.78 times 10 to the -8 which is .0000000178.. The E stands for Exponent and it's the Exponent on 10
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You can submit your drawing for #36d, the cell means plot any way that you can. Paint, for example, is fine. However, it must not be hand drawn.
For question e give the critical range showing Q, r, MSE n' and c, etc., the difference between each pair of means (identifying the means in the context of this problem and not saying X1 - X2) and state which ones (in words in the context of the problem) show a significant difference. For each paired difference I need a statement whether the difference is significant (by comparing the difference to the critical range.)
Tell me if you are using Factor A or Factor B. Remember you only use the Factor for which there is a significant difference. Don't round off the MSE here.
Submit all work by the first post due date. I will point out any mistakes. Then you don't have to do anything. But if you want to improve your grade it will be up to you to reread the lecture and figure out what you need to do to correct your mistake.
Checklist for the written assignment:
1 Calculated F for each
2 Answer to a, b, c in order with Yes or No and reasons
3 cell means plot
4 Factor A or Factor B?
5 Q, n, r, etc. and critical range
6 Paired mean differences identifying the means and not using X's
7 Which pairs show significant difference and answer to f)
Please note: I will point out where your mistakes are, NOT what you must do to fix them. It is your responsibility as part of the learning process, to go over the lecture again. Then you should work the problems in the lecture and compare what you did with what is in the lecture, thereby discovering on your own what needs to be done to fix your mistakes.
Applying the Concepts 36 The operations manager for an appliance manufacturer wants to determine the optimal length of time for the 32Explanation / Answer
Two-way ANOVA: Dirt versus Brand, Cycle
Analysis of Variance for Dirt
Source DF SS MS F P
Brand 3 0.000413 0.000138 0.79 0.519
Cycle 3 0.027338 0.009113 52.07 0.000
Interaction 9 0.002337 0.000260 1.48 0.235
Error 16 0.002800 0.000175
Total 31 0.032888
Individual 95% CI
Brand Mean -----+---------+---------+---------+------
1 0.1463 (------------*-----------)
2 0.1525 (------------*-----------)
3 0.1463 (------------*-----------)
4 0.1425 (-----------*------------)
-----+---------+---------+---------+------
0.1360 0.1440 0.1520 0.1600
Individual 95% CI
Cycle Mean ---+---------+---------+---------+--------
18 0.1037 (--*---)
20 0.1362 (--*---)
22 0.1737 (--*---)
24 0.1737 (--*---)
---+---------+---------+---------+--------
0.1000 0.1250 0.1500 0.1750
Above table gives the output of TWO way ANOVA with 2 observations per cell. Assume that BRAND is treated as TREATMENT and CYCLE TIME (minutes) is BLOCK. Per treatment, per block there are 2 (equal) observations.
From output, it is observed that,
One-way ANOVA: Dirt versus Cycle
Analysis of Variance for Dirt
Source DF SS MS F P
Cycle 3 0.027338 0.009113 45.97 0.000
Error 28 0.005550 0.000198
Total 31 0.032888
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ---+---------+---------+---------+---
18 8 0.10375 0.01685 (---*----)
20 8 0.13625 0.01302 (----*---)
22 8 0.17375 0.00916 (----*---)
24 8 0.17375 0.01598 (----*---)
---+---------+---------+---------+---
Pooled StDev = 0.01408 0.100 0.125 0.150 0.175
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0108
Critical value = 3.86
Intervals for (column level mean) - (row level mean)
18 20 22
20 -0.05171
-0.01329
22 -0.08921 -0.05671
-0.05079 -0.01829
24 -0.08921 -0.05671 -0.01921
-0.05079 -0.01829 0.01921
Above is the output of one way ANOVA with CYCLE TIME as factor and DIRT as response. It is seen that CYCLE TIME has significant effect on DIRT removal (p-value 0.000 < 0.05), in addition, it is also seen that DIRT removal at cycle time 22 and 24 minutes is same.
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