This document discusses statistical confidence interval estimation. It covers: 1) Confidence interval estimation for the mean when the population standard deviation is known and unknown. 2) Confidence interval estimation for the proportion. 3) Factors that affect confidence interval width like data variation, sample size, and confidence level. 4) How to estimate sample sizes needed to estimate a population mean or proportion within a given level of precision and confidence.

1. Statistics for Management 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