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ReviewMGSC272April262010Revised

ReviewMGSC272April262010Revised - Review April 2010...

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Review April 2010 Question 1 A pension fund analyst is investigating pension packages for people working in three sectors: Education, Government, and Industry. The study is conducted in five geographic regions: Atlantic, Quebec, Ontario, Prairie, and BC. Four sample values are selected for each sector- region combination. 1. What are the factors for this study? Factor 1: Sector Factor 2: Region Specify the levels of each factor. Factor 1: Level 1 = Education Level 2 = Government Level 3 = Industry Factor 2: : Level 1 = Atlantic Level 2 = Quebec Level 3 = Ontario Level 4 = Prairie Level 5 = BC 2. What is the total sample size? 3 x 5 x 4 = 60
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3. What type of statistical model is most appropriate for this study? Two-way ANOVA with replication Minitab output is as follows: Two-way ANOVA: Value versus Region, Sector Source DF SS MS F P Region 4 24583 6145.8 16.15 0.000 Sector 2 76471 38235.5 100.50 0.000 Interaction 8 5232 654.0 1.72 0.120 Error 45 17120 380.5 Total 59 123407 4. Test the hypothesis that there is a significant interaction between Region and Sector. Ho: No interaction H 1 : Interaction TS: F = 654/380.5 = 1.72 CV: F .05;8,45 2.18 Conclusion: Do not reject Ho i.e. no significant interaction
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5. Test the hypothesis that the main effect Sector is significant. Ho: µ E = µ G = µ I H 1 : Not all µ are equal TS: F = 38235.5/380.5 = 100.5 CV: F.05;2,45 3.2 Conclusion: Reject Ho => Not all Sector means are equal The Minitab output for Individual 95% CIs is shown below: Individual 95% CIs For Mean Based on Pooled StDev Region Mean -+---------+---------+---------+-------- Atlantic 250.167 (---*----) BC 268.500 (---*----) Ontario 225.750 (---*----) Prairie 245.000 (----*----) Quebec 209.917 (----*----) -+---------+---------+---------+-------- 200 225 250 275 Individual 95% CIs For Mean Based on Pooled StDev Sector Mean -------+---------+---------+---------+-- Education 197.0 (--*--) Government 238.2 (--*--) Industry 284.4 (--*--) -------+---------+---------+---------+-- 210 240 270 300 We see that Industry has the highest values, Government is second and Education is the lowest value.
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6. lthough the interaction is not statistically at the 5% level of significance, the analyst has decided to inspect the interaction plot, and obtained the following result. Quebec Prairie Ontario BC Atlantic 350 300 250 200 150 Region Mean Education Government Industry Sector I nteraction Plot for Value Data Means Would you agree that there is no significant interaction? Explain. Identify any aspect of the graph that might indicate some weak interaction. Overall patterns are very similar, with the following exception: Ontario Prairie - Govt and Industry increase - Education decreases
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Question 2 Based on the scenario of Question 1, suppose the following data were collected: A one-way ANOVA is conducted with the following results: One-way ANOVA: Atlantic, Quebec, Ontario, Prairie, BC Source DF SS MS F P Factor 4 17158 4289 3.79 0.040 Error 10 11312 1131 Total 14 28470 S = 33.63 R-Sq = 60.27% R-Sq(adj) = 44.37% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -----+---------+---------+---------+---- Atlantic 3 240.00 32.79 (--------*--------) Quebec 3 168.67 3.51 (--------*-------) Ontario 3 210.00 36.06 (--------*--------) Prairie 3 231.67 45.37 (-------*--------) BC 3 270.33 34.79 (--------*--------) -----+---------+---------+---------+---- 150 200 250 300 What can you conclude from the above output? Conclude not all 5 means are equal.
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