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Estimation and Testing for Population Proportions Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Point Estimate for a Population Proportion = estimate of p = proportion of sample having a specified attribute Where n = sample size and x = the observed number of successes in the sample Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Confidence Interval for a Population Proportion (small n) Table A.8 Provides 90% and 95% Confidence Interval values Example: n = 15 x = 12 From A.8 a 95 % Confidence Interval p L to p U.519 to.957 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Confidence Interval for a Population Proportion (Large n) (1- ) 100% Confidence Interval Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Choosing the Sample Size With 95% Confidence With E =.02 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion (small n) Obtain (1- ) 100% Confidence Interval Reject H o if p o does not lie between p L and p U Fail to Reject H O if p L p o p U H o : p = p O H a : p p O Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion (small n) Obtain (1-2 ) 100% Confidence Interval Reject H o if p o < p L Fail to Reject H o if p o p L H o : p p o H a : p > p o Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion (small n) Obtain (1-2 ) 100% Confidence Interval Reject H o if p o > p U Fail to Reject H o if p o p U H o : p p o H a : p < p o Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion Two-Tail Test H o : p = p o H a : p p o Reject H o if |Z| > Z /2 Z ˆ p p 0 p 0 (1 p 0 ) n Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion One-Tail Test Z ˆ p p 0 p 0 (1 p 0 ) n H o : p p o H a : p > p o Reject H o if Z > Z Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion One-Tail Test Z ˆ p p 0 p 0 (1 p 0 ) n H o : p p o H a : p < p o Reject H o if Z > - Z Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Confidence Interval for p 1 - p 2 (Large Independent Samples) ˆ Where n 1 p 1, n 1 (1-p 1 ), n 2 p 2, n 2 (1-p 2 ) > 5 ˆˆˆ Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Sample Size Two Populations Where: Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion Two-Tail Test H o : p 1 = p 2 H a : p 1 p 2 Reject H O if |Z| > Z /2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion One-Tail Test H o : p 1 p 2 H a : p 1 > p 2 Reject H o if Z > Z Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Hypothesis Test for Population Proportion One-Tail Test H o : p 1 p 2 H a : p 1 < p 2 Reject H o if Z > - Z Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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Confidence Interval for p 1 - p 2 (Large Independent Samples) ˆ Where n 1 p 1, n 1 (1-p 1 ), n 2 p 2, n 2 (1-p 2 ) > 5 ˆˆˆ Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing
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