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2-6-09 - a The Sampling Distribution of Xbar i In taking...

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Economic Statistics – Class Notes – 2/6/09 NEW TOPIC: II. Estimation of Population Parameters A. Definitions: a. Estimator – A random variable used to estimate a population parameter i. Also known as a sample statistic (a statistic is a characteristic of the sample) ii. The estimator takes on a different value with each sample 1. The estimator is a formula that yields a different value each time a. On average, the estimator will give us an approximation of the population parameter. b. Point Estimate – The specific value the estimator takes on with a given sample c. Interval Estimate – A specific range of values thought to contain the population parameter. i. Usually centered on the point estimate. Parameter Point Estimators B. The properties of ( Xbar ) as an estimator How good a job does ( Xbar ) do in estimating µ

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Unformatted text preview: a. The Sampling Distribution of ( Xbar ) i. In taking samples of size n from some population (the parent population ), it is possible to form a different value of ( Xbar ) with each sample. ii. The sampling distribution for ( Xbar ) is the probability distribution of all values ( Xbar ) can take on. 1. Each value of Xbar will have a probability associated with it. Example: Parent Population X1 = 1 X2 = 3 X3 = 3 X4 = 5 X5 = 5 µ = Sum(Xi/N) from i=1 to 5 = (17/5) = 3.4 Consider all samples of size 2: Observation Hypothetical Sample Actual Sample Sample Mean 1 X1, X2 1, 3 2 2 X1, X3 1, 3 2 3 X1, X4 1, 5 (X4 = 5) 3 4 X1, X5 1, 5 (a different 5 X5 = 5) 3 5 X2, X3 3, 3 3 6 X2, X4 3, 5 4 7 X2, X5 3, 5 4 8 X3, X4 3, 5 4 9 X3, X5 3, 5 4 10 X4, X5 5, 5 5 All observations have N = 2...
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2-6-09 - a The Sampling Distribution of Xbar i In taking...

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