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Inference about Variances Sampling Distribution of Variances : You want to know the variance of a population. But you realize the population is too large to actually compute the true variance. So you decide to observe a sample from the population and use the sample variance as an estimate of the population variance. You need the sampling distribution of the sample variance in order to make inference about the population variance. The population is normally distributed with mean μ and standard deviation σ . Let y denote an observation from the population. Draw sample of size n . 12 ,, n yy y K Compute the sample variance 2 2 () 1 i i s n = . Then sampling distribution of (n-1)s 2 / σ 2 is chi-square with n-1 degrees of freedom. 1

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Inference about Variances Use the table for the chi-square distribution or a computer program to get probabilities. Examples: Suppose X has chi-square distribution with df=4.
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