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Unformatted text preview: lecture 13, Samples and Surveys, Sampling Distributions I 1/21 Samples and Surveys Sampling Distribution Sampling Distribution of the Sample Mean Central Limit Theorem (CLT) lecture 13, Samples and Surveys, Sampling Distributions I Outline 1 Samples and Surveys 2 Sampling Distribution Sampling Distribution of the Sample Mean 3 Central Limit Theorem (CLT) lecture 13, Samples and Surveys, Sampling Distributions I 2/21 Samples and Surveys Sampling Distribution Sampling Distribution of the Sample Mean Central Limit Theorem (CLT) lecture 13, Samples and Surveys, Sampling Distributions I Samples and Surveys Samples • Want to learn some numerical facts about a population (called population parameters , e.g., μ , σ ) • 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. • Examine part of the population, called the sample , and make inferences from the sample about the population • Parameters are estimated by sample statistics , i.e., numbers which can be computed from a sample (e.g., ¯ x , s ) Estimate = Parameter + Bias + Chance Error • Bias: systematic error in an estimate. Bias should be avoided as much as possible in survey, by choosing samples that reflect the mix in the entire population (be representative ) • How sample is chosen matters a lot. lecture 13, Samples and Surveys, Sampling Distributions I 3/21 Samples and Surveys Sampling Distribution Sampling Distribution of the Sample Mean Central Limit Theorem (CLT) lecture 13, Samples and Surveys, Sampling Distributions I Samples and Surveys The Literary Digest Case, revisited • 1936 election: Roosevelt vs Landon; • Roosevelt’s percentage: The Digest prediction: 43%; The election result: 62%; • Literary Digest interviewed 2.4 million potential voters (the largest number of people ever replying to a poll!) (total voted: about 45 million) • Literary Digest went bankrupt soon after the 1936 presidential election... • In contrast, Gallup interviewed only 50,000 people, and correctly forecast the Roosevelt victory ( Gallup predicted 56%). lecture 13, Samples and Surveys, Sampling Distributions I 4/21 Samples and Surveys Sampling Distribution Sampling Distribution of the Sample Mean Central Limit Theorem (CLT) lecture 13, Samples and Surveys, Sampling Distributions I Samples and Surveys Example, The Literary Digest, revisited, ctd Q: What went wrong with Literary Digest ’s method? • Literary Digest ’s sampling procedure: mailed questionnaires to 10 million people on telephone books and club membership lists, about 24% responded; I Mistake #1: in 1936, poor people were more likely not to have telephones or join clubs; • Systematic tendency in the sampling procedure to exclude one kind of person or another from the sample — selection bias ; I Mistake #2: about 76% surveyed people did not respond, and only the respondents were taken into account....
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This note was uploaded on 12/28/2010 for the course BUSINESS A ISOM 111 taught by Professor Yingyingli during the Fall '10 term at HKUST.
 Fall '10
 YingYingLi
 Business

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