Chp14-Module 14 - Population Standard Deviation

Chp14-Module 14 - Population Standard Deviation - Module 14...

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1 Module 14 Inferences for Population Standard Deviations Objectives: One should be able to construct confidence intervals for a population standard deviation or the ratio or two std. deviations perform hypothesis tests for a population standard deviation or the ratio or two std. deviations Recall: For z-tests we claim to ‘KNOW’ the population standard deviation. For pooled two-sample t-test we claim to ‘KNOW’ that the std. deviations were equal. How can we validate this claims?

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Strategy: • Select an estimator (statistic) of the population standard deviation (or variance) • Determine its probability distribution • Use the distribution to determine critical values or p-values for hypothesis tests • Use the distribution to determine confidence intervals Statistic : Sample Variance 2 2 ( ) 1 x x S n - = - or ( ) 2` 2 / 1 x x n n - = - Sampling Distribution : The quantity defined by has a chi-square distribution with n-1 degrees of freedom. 2
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This note was uploaded on 09/26/2009 for the course OM 550 taught by Professor Kin during the Spring '09 term at Universidad Católica del Maule.

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Chp14-Module 14 - Population Standard Deviation - Module 14...

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