2. Copyright © 2011 Pearson Education, Inc. Samples and Surveys Chapter 13

3. 13.1 Two Surprising Properties of Sampling How is the winning car model of J.D. Power and Associates Initial Quality Award determined?  By focusing on a subset of the whole group (a sample)  By making sure that items are selected randomly from the larger group Copyright © 2011 Pearson Education, Inc. 3 of 36

4. 13.1 Two Surprising Properties of Sampling Definitions  Population: the entire collection of interest  Sample: subset of the population  Survey: posing questions to a sample to learn about the population  Representative: samples that reflect the mix in the entire population  Bias: systematic error in selecting the sample Copyright © 2011 Pearson Education, Inc. 4 of 36

5. 13.1 Two Surprising Properties of Sampling The two surprises are:  The best way to get a representative sample is to pick members of the population at random.  Larger populations do not require larger samples. Copyright © 2011 Pearson Education, Inc. 5 of 36

6. 13.1 Two Surprising Properties of Sampling Randomization  A randomly selected sample is representative of the whole population.  Randomization ensures that on average a sample mimics the population. Copyright © 2011 Pearson Education, Inc. 6 of 36

7. 13.1 Two Surprising Properties of Sampling Comparison of Two Random Samples from a Population of 3.5 Million Customers. Copyright © 2011 Pearson Education, Inc. 7 of 36

8. 13.1 Two Surprising Properties of Sampling Randomization  Produces samples whose averages resemble those in the population (avoids bias).  Enables us to infer characteristics of the population from a sample. Copyright © 2011 Pearson Education, Inc. 8 of 36

9. 13.1 Two Surprising Properties of Sampling Infamous Case: The Literary Digest The Literary Digest predicted defeat for Franklin D. Roosevelt in the 1936 presidential election. They selected their sample from a list of telephone numbers (telephones were a luxury during the Great Depression). Roosevelt’s supporters tended to be poor and were underrepresented in the sample. Copyright © 2011 Pearson Education, Inc. 9 of 36

10. 13.1 Two Surprising Properties of Sampling This sample size is an almost infinitesimal portion of the population, yet the survey reveals attitudes of the entire population to within ± 3% Copyright © 2011 Pearson Education, Inc. 10 of 36

11. 13.1 Two Surprising Properties of Sampling Simple Random Sample (SRS)  A sample of n items chosen by a method that has an equal chance of picking any sample of size n from the population.  Is the standard to which all other sampling methods are compared. Copyright © 2011 Pearson Education, Inc. 11 of 36

12. 13.1 Two Surprising Properties of Sampling Simple Random Sample (SRS)  Sampling Frame: a list of items from which to select a random sample.  Systematic Sampling: method for selecting items from a sampling frame that follows a regular pattern (e.g., every 10 th item). Copyright © 2011 Pearson Education, Inc. 12 of 36

13. 13.1 Two Surprising Properties of Sampling Identifying the Sampling Frame  If there is no fixed population of outcomes, no sampling frame exists (e.g., output from a production process).  The list available may differ from the list desired (e.g., voter registration lists identify people who can vote, not those who will). Copyright © 2011 Pearson Education, Inc. 13 of 36

14. 13.2 VARIATION Estimating Parameters  Parameter: a characteristic of the population (e.g., µ)  Statistic: an observed characteristic of a sample (e.g., )  Estimate: using a statistic to approximate a parameter Copyright © 2011 Pearson Education, Inc. 14 of 36

15. 13.2 VARIATION Notation for Statistics and Parameters Copyright © 2011 Pearson Education, Inc. 15 of 36

16. 13.2 VARIATION Sampling Variation  Is the variability in the value of a statistic from sample to sample.  The price we pay for working with a sample rather than the population. Copyright © 2011 Pearson Education, Inc. 16 of 36

17. 13.2 VARIATION Sampling Variation in Sample Means Copyright © 2011 Pearson Education, Inc. 17 of 36

18. 13.2 VARIATION Sampling Variation in Sample Proportions Copyright © 2011 Pearson Education, Inc. 18 of 36

19. 4M Example 13.1: EXIT SURVEYS Motivation Why do customers leave a busy clothing store in the mall without making a purchase? Copyright © 2011 Pearson Education, Inc. 19 of 36

20. 4M Example 13.1: EXIT SURVEYS Method A survey is necessary. The owner decides to survey 50 weekend customers. The ideal sampling frame would list every customer who did not make a purchase over the weekend. Such a list does not exist. Copyright © 2011 Pearson Education, Inc. 20 of 36

21. 4M Example 13.1: EXIT SURVEYS Mechanics Interview every 10 th customer who departs the store on the weekend. Based on typical customer flow, a sample of size 60 is expected. Ask customers why they didn’t make a purchase. Copyright © 2011 Pearson Education, Inc. 21 of 36

22. 4M Example 13.1: EXIT SURVEYS Message On the basis of the survey, the owner will be able to find out why shoppers are leaving without buying. Copyright © 2011 Pearson Education, Inc. 22 of 36

23. 13.3 ALTERNATIVE SAMPLING METHODS Stratified Samples  Divide the sampling frame into homogeneous groups, called strata  Use simple random sample to select items from each strata Copyright © 2011 Pearson Education, Inc. 23 of 36

24. 13.3 ALTERNATIVE SAMPLING METHODS Cluster Samples  Divide a geographic region into clusters  Randomly select clusters  Randomly choose items within selected clusters Copyright © 2011 Pearson Education, Inc. 24 of 36

25. 4M Example 13.2: ESTIMATING THE RISE OF PRICES Motivation What goes into determining the consumer price index (CPI), the official measure of inflation? Copyright © 2011 Pearson Education, Inc. 25 of 36

26. 4M Example 13.2: ESTIMATING THE RISE OF PRICES Method The Bureau of Labor Statistics (BLS) uses a survey to estimate inflation. The target population consists of the costs of every consumer transaction in urban areas during a specific month. Copyright © 2011 Pearson Education, Inc. 26 of 36

27. 4M Example 13.2: ESTIMATING THE RISE OF PRICES Mechanics The BLS has a list of urban areas and a list of people living in each, but does not have a list of every sales transaction. So the BLS divides items sold into 211 categories and estimates the change in price for each category in every area. Copyright © 2011 Pearson Education, Inc. 27 of 36

28. 4M Example 13.2: ESTIMATING THE RISE OF PRICES Message The urban consumer price index is an estimate of inflation base on a complex, clustered sample in selected metropolitan areas. Copyright © 2011 Pearson Education, Inc. 28 of 36

29. 13.3 ALTERNATIVE SAMPLING METHODS Census  A comprehensive survey of the entire population.  Cost and time constraints generally prohibit carrying out a census; in some cases a census is not feasible. Copyright © 2011 Pearson Education, Inc. 29 of 36

30. 13.3 ALTERNATIVE SAMPLING METHODS Voluntary Response  A sample consisting of individuals who volunteer when given the opportunity to participate in a survey.  These samples are biased toward those with strong opinions. Copyright © 2011 Pearson Education, Inc. 30 of 36

31. 13.3 ALTERNATIVE SAMPLING METHODS Convenience Samples  A sampling method that selects individuals who are readily available.  Although easy to obtain, these samples are rarely representative. Copyright © 2011 Pearson Education, Inc. 31 of 36

32. 13.4 CHECKLIST FOR SURVEYS Questions to Consider  What was the sampling frame?  Is the sample a simple random sample?  What is the rate of nonresponse?  How was the question worded?  Did the interviewer affect the results?  Does survivor bias affect the survey? Copyright © 2011 Pearson Education, Inc. 32 of 36

33. 13.4 CHECKLIST FOR SURVEYS How Wording of the Question Affects Results Copyright © 2011 Pearson Education, Inc. 33 of 36

34. Best Practices  Randomize.  Plan carefully.  Match the sampling frame to the target population. Copyright © 2011 Pearson Education, Inc. 34 of 36

35. Best Practices (Continued)  Keep focused.  Reduce the amount of nonresponse.  Pretest your survey. Copyright © 2011 Pearson Education, Inc. 35 of 36

36. Pitfalls  Don’t conceal flaws in your sample.  Do not lead the witness.  Do not confuse a sample statistic for the population parameter.  Do not accept results because they agree with what you expect. Copyright © 2011 Pearson Education, Inc. 36 of 36