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# LCT11 - 1 Introduction to Business Statistics Lecture 11...

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Unformatted text preview: 1 Introduction to Business Statistics Lecture 11 Computation of Confidence Intervals From Bounds on Error of Estimation to Confidence Intervals: Intervals Confidence ) 96 . 1 96 . 1 ( Estimation of Error ) 96 . 1 96 . 1 ( on Distributi Sampling ) 96 . 1 96 . 1 ( 95 . n X n X P n X n P n X n P σ μ σ σ μ σ σ μ σ μ + ≤ ≤ − = ≤ − ≤ − = + ≤ ≤ − = 2 A )% 1 ( 100 α − Confidence Interval : n z x z x x σ σ α α 2 / 2 / ± = ± • Lower confidence limit: n z x z x x σ σ α α 2 / 2 / − = − • Upper confidence limit: n z x z x x σ σ α α 2 / 2 / + = + • Confidence coefficient: ) 1 ( α − • Critical value 2 / α z : 2 / } { 2 / α α = > z Z P , the value that cuts off a right tail probability of 2 / α from the standard norm distribution. ⎪ ⎩ ⎪ ⎨ ⎧ = = − = = − = = − = 0.5% 2 / or 99% 1 if 2.58 2.5% 2 / or 95% 1 if 1.96 5% 2 / or 90% 1 if 1.645 2 / α α α α α α α z 3 Interpretation of confidence coefficient: After obtaining a 95% confidence interval from a given sample (a pair...
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LCT11 - 1 Introduction to Business Statistics Lecture 11...

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