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ECON 4630 ECON 5630 TOPIC #6: SAMPLING I. Introduction and Motivation A. General B. Why Is Sampling Necessary? 1 II. Probability Sampling Methods A. Probability vs. Non-Probability Sampling B. Types of Probability Sampling 1. Simple Random Sampling 2. Systematic Random Sampling 2 3. Stratified Random Sampling 4. Stratified Cluster Sampling 3 4 III. Sampling Error and Sampling Distributions A. Definition: sampling error is the difference between a sample estimate and the corresponding population parameter. B. Sampling Distributions Imagine drawing samples from a given population over and over again. If we calculate X each time, we’ll slowly put together a probability distribution of the sample means. Here’s an extended example: Executive’s Name Snow Years of Service 20 Tolson 22 Kraft 26 Irwin 24 Jones 28 What’s the population mean? 5 Now suppose we draw samples of 2 from this population. There are 5! 10 different possibilities for samples: 2!(5 2)! Sample Snow Tolson Snow Kraft Snow Irwin Snow Jones Tolson Kraft Tolson Irwin Tolson Jones Kraft Irwin Kraft Jones Irwin Jones Sample Mean In histogram form: 6 Points to note: What is the mean of the means? How does it compare with the population mean? What is the shape of the distributions of sample means? IV. The Central Limit Theorem: In repeated random samples of a particular size, the sampling distribution of the sample means is distributed approximately normal, with mean = and standard deviation of V. n . (If is unknown, we use our estimate of it, S) Excel Commands To generate random numbers between 0 and 1, use =RAND(). To generate random numbers between a and b, use =RANDBETWEEN(a,b). 7 NOTES: 8