1. Chap 7-1 Basic Business Statistics (10 th Edition) Chapter 7 Sampling Distributions

2. Chap 7-2 Chapter Topics Sampling Distribution of the Mean The Central Limit Theorem Sampling Distribution of the Proportion Sampling from Finite Population

3. Chap 7-3 Why Study Sampling Distributions Sample Statistics are Used to Estimate Population Parameters E.g., estimates the population mean Problem: Different Samples Provide Different Estimates Large sample gives better estimate; large sample costs more How good is the estimate? Approach to Solution: Theoretical Basis is Sampling Distribution

4. Chap 7-4 Sampling Distribution Theoretical Probability Distribution of a Sample Statistic Sample Statistic is a Random Variable Sample mean, sample proportion Results from Taking All Possible Samples of the Same Size

5. Chap 7-5 Developing Sampling Distributions Suppose There is a Population … Population Size N=4 Random Variable, X, is Age of Individuals Measured in Years Values of X : 18, 20, 22, 24 A B C D

6. Chap 7-6.3.2.1 0 A B C D (18) (20) (22) (24) Uniform Distribution P(X) X Developing Sampling Distributions (continued) Summary Measures for the Population Distribution

7. © 2004 Prentice-Hall, Inc. Chap 7-7 All Possible Samples of Size n=2 N n = 4 2 = 16 Samples Taken with Replacement 16 Sample Means Developing Sampling Distributions (continued)

8. © 2004 Prentice-Hall, Inc. Chap 7-8 Sampling Distribution of All Sample Means 18 19 20 21 22 23 24 0.1.2.3 X Sample Means Distribution 16 Sample Means _ Developing Sampling Distributions (continued)

9. Chap 7-9 Summary Measures of Sampling Distribution Developing Sampling Distributions (continued)

10. Chap 7-10 Comparing the Population with Its Sampling Distribution 18 19 20 21 22 23 24 0.1.2.3 X Sample Means Distribution n = 2 A B C D (18) (20) (22) (24) 0.1.2.3 Population N = 4 X _

11. Chap 7-11 Properties of Summary Measures I.e., is unbiased Standard Error (Standard Deviation) of the Sampling Distribution is Less Than the Standard Error of Other Unbiased Estimators For Sampling with Replacement or without Replacement from Large or Infinite Populations: As n increases, decreases

12. Chap 7-12 Unbiasedness ( ) Unbiased

13. Chap 7-13 Less Variability Sampling Distribution of Median Sampling Distribution of Mean Standard Error (Standard Deviation) of the Sampling Distribution is Less Than the Standard Error of Other Unbiased Estimators

14. Chap 7-14 Effect of Large Sample Larger sample size Smaller sample size

15. Chap 7-15 When the Population is Normal Central Tendency Variation Population Distribution Sampling Distributions

16. Chap 7-16 When the Population is Not Normal Central Tendency Variation Population Distribution Sampling Distributions

17. Chap 7-17 Central Limit Theorem As Sample Size Gets Large Enough Sampling Distribution Becomes Almost Normal Regardless of Shape of Population

18. Chap 7-18 How Large is Large Enough? For Most Distributions, n>30 For Fairly Symmetric Distributions, n>15 For Normal Distribution, the Sampling Distribution of the Mean is Always Normally Distributed Regardless of the Sample Size This is a property of sampling from a normal population distribution and is NOT a result of the central limit theorem

19. Chap 7-19 Example: Sampling Distribution Standardized Normal Distribution

20. Chap 7-20 Population Proportion Categorical Variable E.g., Gender, Voted for Bush, College Degree Proportion of Population Having a Characteristic Sample Proportion Provides an Estimate If Two Outcomes, X Has a Binomial Distribution Possess or do not possess characteristic

21. Chap 7-21 Sampling Distribution of Sample Proportion Approximated by Normal Distribution Mean: Standard error: p = population proportion Sampling Distribution f(p s ).3.2.1 0 0. 2.4.6 8 1 psps

22. Chap 7-22 Standardizing Sampling Distribution of Proportion Sampling Distribution Standardized Normal Distribution

23. Chap 7-23 Example: Sampling Distribution Standardized Normal Distribution

24. Chap 7-24 Sampling from Finite Population (CD ROM Topic) Modify Standard Error if Sample Size (n) is Large Relative to Population Size (N ) Use Finite Population Correction Factor (FPC) Standard Error with FPC

25. Chap 7-25 Chapter Summary Discussed Sampling Distribution of the Sample Mean Described the Central Limit Theorem Discussed Sampling Distribution of the Sample Proportion Described Sampling from Finite Populations