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Unformatted text preview: Sampling and Point Estimation GE331 / IE300 G. Köksal UIUC, IESE, 2011 2 Contents • Simple random sampling • Point estimator vs. point estimate • Accuracy vs. precision • Sampling distributions • Some properties of estimators • Mean squared error • Standard error • Methods of point estimation: Maximum likelihood method • Some other methods of sampling 3 Sampling and Estimates • The reason we select a sample is to collect data to answer a research question about a population. • The sample results provide only estimates of the values of the population characteristics. • With proper sampling methods, the sample results can provide “good” estimates of the population characteristics. 4 Sampling From a Finite Population • Finite populations are often defined by lists such as: – Credit card account numbers – Inventory product numbers – Class membership roster • A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size n has the same probability of being selected. 5 Sampling From a Finite Population • Replacing each sampled element before selecting subsequent elements is called sampling with replacement. • Sampling without replacement is the procedure used most often. • In large sampling projects, computergenerated random numbers are often used to automate the sample selection process. 6 Sampling From a Finite Population • Example: A simple random sample of 10 students from the Engineering College undergraduates of 6628 students can be selected as follows: 1. Assign a random number to each of the 6628 students generated using Excel’s RAND function (U(0,1)) 2. Select the 10 applicants corresponding to the 10 smallest random numbers. 7 Sampling From an Infinite Population • Populations are often generated by an ongoing process where there is no upper limit on the number of units that can be generated. • Some examples of ongoing processes, with infinite populations, are: • parts being manufactured on a production line • transactions occurring at a bank • telephone calls arriving at a call center • customers entering a store 8 Sampling From an Infinite Population • A random sample from an infinite population is a sample selected such that the following...
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 Spring '09
 Zafarani
 Standard Deviation, Estimation theory, Bias of an estimator

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