Q 1b18. Nico Case, the Industrial Engineer from Company, has just completed an e
ID: 2907658 • Letter: Q
Question
Q 1b18. Nico Case, the Industrial Engineer from Company, has just completed an experiment with five different scenarios. She has run her scenarios for five different replications, each of 12 months. She obtains the following output, which represents monthly throughput:
Scenario
1
Scenario
2
Scenario
3
Scenario
4
Scenario
5
3993
3979
3965
4007
4052
3992
3999
3988
4006
4125
4007
4021
4017
3991
4013
4010
4015
3971
3995
4014
3988
4000
4025
3994
4042
19990
20014
19966
19993
20246
SUM
3998.0
4002.8
3993.2
3998.6
4049.2
AVERAGE
96.5
267.2
723.2
54.3
2088.7
VARIANCE
a) Which, if any, of the scenarios is provably the best (where larger is better)? Use an alpha ? of 0.05.
b) Outline all assumptions that underlie your analysis in (a).
c) There are at least two ways of analyzing the data set above to determine which of the policies is best. Identify one other method for completing this analysis. Describe in your own words (but do not calculate) how you would complete this other analysis?
To aid you in your calculations, you may assume that the overall sum of the data is 100,209 and that the sample average is 4008 with a variance of 982.3233.
Scenario
1
Scenario
2
Scenario
3
Scenario
4
Scenario
5
3993
3979
3965
4007
4052
3992
3999
3988
4006
4125
4007
4021
4017
3991
4013
4010
4015
3971
3995
4014
3988
4000
4025
3994
4042
19990
20014
19966
19993
20246
SUM
3998.0
4002.8
3993.2
3998.6
4049.2
AVERAGE
96.5
267.2
723.2
54.3
2088.7
VARIANCE
Explanation / Answer
Nico Case, the Industrial Engineer from Company, has just completed an experiment with five different scenarios. Cleaarly the data has been classified according to only one factor namely the scenario.
So an appropriate design to study the effect of each of scenarios would be a Completely Randomised Design or One Way ANOVA (Analysis of Variance).
Our test of hypothesis shall be :
Ho : all scenarios are the same vs H1 : all scenarios are not the same
The analysis can be presented in the form of a table as follows :-
We see that at 5% level of significance, the observed p value (0.013482) < 0.05.
Hence we may conclude that the scenarios vary signiificantly, and so we reject the null hypothesis at alpha=0.05.
By carefully observing the means of the different scenarios it can be well estimated that scenmario 5 is probably the best.
The underlying assumptions in our test :
The observations were independently drawn and have a common variance.
Groups Count Sum Average Variance 1 5 19990 3998 96.5 2 5 20014 4002.8 267.2 3 5 19966 3993.2 723.2 4 5 19993 3998.6 54.3 5 5 20246 4049.2 2088.7 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 10656.16 4 2664.04 4.124029 0.013482 2.866081 Within Groups 12919.6 20 645.98 Total 23575.76 24Related Questions
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