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.

Answer 1

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 :-

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	24

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.