1. Estimation and Testing for Population Proportions Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

2. 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

3. 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

4. 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

5. Choosing the Sample Size With 95% Confidence With E =.02 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Sample Size Two Populations Where: Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

14. 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

15. 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

16. 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

17. 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