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Slides-12 - ECON1203/ECON2292 Business and Economic...

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Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 12
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22 Week 12 topics l Chi-squared distribution l Hypothesis test for a population variance l Chi-squared test of goodness of fit l Chi-squared test of a contingency table l Key references l Keller 12.2, 15.1-15.2
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33 Some different problems l Previously have concentrated on inference associated with location problems l Means, proportions & conditional means (regression) l Many other interesting statistical problems l P1: CPRepairs has fluctuating demand for vehicle repairs necessitating paying staff overtime l Changing variability could present peak load problems for staff availability &/or morale l Inference problem: Has there been a change in the variance of total overtime hours?
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44 Some different problems… l P2: CPRepairs concerned about consumer satisfaction with service l Industry benchmarks for satisfaction levels are available l Inference problem: Do CPRepairs survey results differ from industry benchmarks? l P3: CPRepairs services a range of customer types (private, business, government) l If split customer satisfaction results by type can we observe differences? l Inference problem: Is customer satisfaction independent of customer type?
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55 Hypotheses about variances l In testing hypotheses about variances obvious test statistic is based on s 2 l In order to compare s 2 with σ 2 need appropriate sampling distribution l Need to consider a new distribution
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66 Hypotheses about variances…
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P1: CPRepairs overtime l Staff numbers set assuming total of 50 hours overtime per week & variance of 25 l Is there evidence of a different variance?
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