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Unformatted text preview: AMS 315 Data Analysis Chapter Seven Study Guide Inferences about Population Variances Fall 2010 Context The variance of a random variable is a critical parameter in assessing risk and the extent to which the expected value of the random variable is known. Having a confidence interval for the population variance is a potentially useful tool. Since the two independent sample equal variance t-test assumes equal variances, it is logical to ask for a test of equality of variances. Standard statistical theory (specifically a procedure called the likelihood ratio test) suggests the ratio of sample variances is a good test. In practice, the procedures given in this chapter are of limited value because the distributions of the test statistics are very sensitive to the assumption of normality. Specifically, the percentiles of the null distribution of the test statistics increase as the kurtosis of the sampled random variable increases. The procedures are of value for two reasons. First, the distribution of many random variables encountered in practice is reasons....
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- Fall '08