1. Statistics for Management Lesson 4 Confidence Interval Estimation

3. Mean,  , is unknown Population Random Sample I am 95% confident that  is between 40 & 60. Mean X = 50 Estimation Process Sample

4. Estimate Population Parameter... with Sample Statistic Mean  Proportion p p s Variance s 2 Population Parameters Estimated  2 Difference  -  1 2 x - x 1 2 X _ _ _

6. Confidence Interval Sample Statistic Confidence Limit (Lower) Confidence Limit (Upper) A Probability That the Population Parameter Falls Somewhere Within the Interval. Elements of Confidence Interval Estimation

7. Parameter = Statistic ± Its Error © 1984-1994 T/Maker Co. Confidence Limits for Population Mean Error = Error = Error Error

8. 90% Samples 95% Samples Confidence Intervals 99% Samples X _  x _

10. Confidence Intervals Intervals Extend from (1 -  ) % of Intervals Contain  .   % Do Not. 1 -   /2  /2 X _  x _ Intervals & Level of Confidence Sampling Distribution of the Mean to

12. Mean  Unknown Confidence Intervals Proportion Finite Population  Known Confidence Interval Estimates

14. Mean  Unknown Confidence Intervals Proportion Finite Population  Known Confidence Interval Estimates

16. Z t 0 t ( df = 5) Standard Normal t ( df = 13) Bell-Shaped Symmetric ‘ Fatter’ Tails Student’s t Distribution

18. Upper Tail Area df .25 .10 .05 1 1.000 3.078 6.314 2 0.817 1.886 2.920 3 0.765 1.638 2.353 t 0 Assume: n = 3 df = n - 1 = 2   = .10  /2 =.05 2.920 t Values  / 2 .05 Student’s t Table

20. Mean  Unknown Confidence Intervals Proportion Finite Population  Known Confidence Interval Estimates

22. Mean  Unknown Confidence Intervals Proportion Finite Population  Known Confidence Interval Estimates