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

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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

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

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

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

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

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

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

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

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

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

13.1 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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