OHCh5-A

# OHCh5-A - Chapter 5: Con dence Interval Estimation and...

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Testing Lecture 1 This chapter is based on Studendmund’s Chapter 5 entitled "Hypothesis the title of the chapter for the lectures on this chapter because I want to emphasize con&dence intervals are a form of estimation.

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1 The Normal Distribution Read Section 16.1.5 (p.545) in Studenmund if you are not familiar with the normal distribution. See Figures 16.4 and 16.5. 1.1 Properties of the Normal Distribution Let X be a normally distributed random variable with mean and variance ± 2 .
(1) The normal distribution is symmetrical around its mean, . (2) See Figure 16.6 for the shape of the Normal Distribution. It has a symmetric bell shape. (3) A normal distribution is fully described by and ± 2 . (4) A linear combination of two or more normally distributed random vari- ables is normally distributed. 1.2 The Standard Normal Distribution Normally distributed random variables have di&erent shapes of probabil- ity distributions, depending on and ± 2 . Suppose that X is normally distributed with mean , and ± 2 . Then

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Z = X ± (1) has the standard normal distribution , that is, Z is normally distributed with mean zero and unit variance. 1.3 The Sampling Distribution of the Sample Mean Read Studenmund’s Section 16.3 if you are not familiar with the sampling distributions of the sample mean.
Before studying the sampling distributions of the OLS estimators, let us mean is the OLS estimator for population mean if we let Y i = + ± i (2) where ± i

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## This note was uploaded on 07/17/2008 for the course ECON 444 taught by Professor Ogaki during the Fall '07 term at Ohio State.

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OHCh5-A - Chapter 5: Con dence Interval Estimation and...

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