Lesson04_Static11
- 1. Statistics for Management Confidence Interval Estimation
- 2. Lesson Topics Confidence Interval Estimation for the Mean ( Known) Confidence Interval Estimation for the Mean ( Unknown) Confidence Interval Estimation for the Proportion The Situation of Finite Populations Sample Size 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 _ _ _
- 5. Provides Range of Values Based on Observations from 1 Sample Gives Information about Closeness to Unknown Population Parameter Stated in terms of Probability Never 100% Sure Confidence Interval Estimation
- 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 _
- 9. Probability that the unknown population parameter falls within the interval Denoted (1 - ) % = level of confidence e.g. 90%, 95%, 99% Is Probability That the Parameter Is Not Within the Interval Level of Confidence
- 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
- 11. Data Variation measured by Sample Size Level of Confidence (1 - ) Intervals Extend from © 1984-1994 T/Maker Co. Factors Affecting Interval Width X - Z to X + Z x x
- 12. Mean Unknown Confidence Intervals Proportion Finite Population Known Confidence Interval Estimates
- 13. Assumptions Population Standard Deviation Is Known Population Is Normally Distributed If Not Normal, use large samples Confidence Interval Estimate Confidence Intervals ( Known)
- 14. Mean Unknown Confidence Intervals Proportion Finite Population Known Confidence Interval Estimates
- 15. Assumptions Population Standard Deviation Is Unknown Population Must Be Normally Distributed Use Student’s t Distribution Confidence Interval Estimate Confidence Intervals ( Unknown)
- 16. Z t 0 t ( df = 5) Standard Normal t ( df = 13) Bell-Shaped Symmetric ‘ Fatter’ Tails Student’s t Distribution
- 17. Number of Observations that Are Free to Vary After Sample Mean Has Been Calculated Example Mean of 3 Numbers Is 2 X 1 = 1 (or Any Number) X 2 = 2 (or Any Number) X 3 = 3 (Cannot Vary) Mean = 2 degrees of freedom = n -1 = 3 -1 = 2 Degrees of Freedom ( df )
- 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
- 19. A random sample of n = 25 has = 50 and s = 8. Set up a 95% confidence interval estimate for . . . 46 69 53 30 Example: Interval Estimation Unknown
- 20. Mean Unknown Confidence Intervals Proportion Finite Population Known Confidence Interval Estimates
- 21. Assumptions Sample Is Large Relative to Population n / N > .05 Use Finite Population Correction Factor Confidence Interval (Mean, X Unknown) X Estimation for Finite Populations
- 22. Mean Unknown Confidence Intervals Proportion Finite Population Known Confidence Interval Estimates
- 23. Assumptions Two Categorical Outcomes Population Follows Binomial Distribution Normal Approximation Can Be Used n · p 5 & n· (1 - p ) 5 Confidence Interval Estimate Confidence Interval Estimate Proportion
- 24. A random sample of 400 Voters showed 32 preferred Candidate A. Set up a 95% confidence interval estimate for p . p .053 .107 Example: Estimating Proportion
- 25. Sample Size Too Big: Requires too much resources Too Small: Won’t do the job
- 26. What sample size is needed to be 90% confident of being correct within ± 5 ? A pilot study suggested that the standard deviation is 45. n Z Error 2 2 2 2 2 2 1 645 45 5 219 2 220 . . Example: Sample Size for Mean Round Up
- 27. What sample size is needed to be within ± 5 with 90% confidence? Out of a population of 1,000, we randomly selected 100 of which 30 were defective. Example: Sample Size for Proportion Round Up 228
- 28. What sample size is needed to be 90% confident of being correct within ± 5 ? Suppose the population size N = 500. Example: Sample Size for Mean Using fpc Round Up where 153
- 29. Lesson Summary Discussed Confidence Interval Estimation for the Mean ( Known) Discussed Confidence Interval Estimation for the Mean ( Unknown) Addressed Confidence Interval Estimation for the Proportion Addressed the Situation of Finite Populations Determined Sample Size