201 Lectures 1 - Unit 1: Basic Concepts of Inference...

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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 1 Statistics 201: Introduction to Statistics Ramón V. León Unit 1: Basic Concepts of Inference
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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 2 Statistical Inference Deals with methods for making statements about a population based on a sample drawn from the population Estimation: Estimating an unknown population parameter Hypothesis testing: Testing a hypothesis about an unknown population parameter Examples Estimation: Estimating the mean package weight of a cereal box filled during a production shift Hypothesis testing: Do the cereal boxes meet the minimum mean weight specification of 16 oz? Inference Informal using summary statistics Formal which uses methods of probability and sampling distributions to develop measures of statistical accuracy
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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 3 Estimation Problems Point estimation: Estimation of an unknown population parameter by a single statistic calculated from the sample data Confidence interval estimation: Calculation of an interval from sample data that includes the unknown population parameter with a preassigned probability
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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 4 Point Estimation Let X 1 , X 2 , …, X n be a random sample from a population with an unknown parameter θ . A point estimator ˆ of θ is a statistic computed from sample data 1 ˆ is anestimator of n i i X X n θμ = = == () 2 22 1 ˆ is anestimator of 1 n i i XX S n θσ = = is a r.v. because it is a function of the X i s which are r.v.’s ˆ Examples:
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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 5 Bull’s Eye Analogy
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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 6 Standard Error (SE) The standard deviation of an estimator is called the standard error of the estimator The estimated standard error is also often called standard error (SE) The precision of an estimator (or estimate?) is measured by the SE Example 1 : is an unbiased estimator of X μ () SE X n σ = ( ) estimated SE X s n = standard error of the mean (SEM) ˆˆ (1 ) is an unbiased estimator of and ( ) pp S E p n = Example 2 :
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3/25/2008 Unit 1 - Stat 201 - Ramón V. León 7 Precision and Standard Error A precise estimate has a small standard error, but exactly how are the precision and standard error related?
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201 Lectures 1 - Unit 1: Basic Concepts of Inference...

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