# solution

Let 1, 2,. . ., n and 1, 2,. . ., m be two . . . samples with sample variances x and y respectively. A confidence interval for the equivalence of sample variances can be given from the following statistic: If the underlying i and i are normally distributed, then the distribution of Â is known to be the -distribution with Â âˆ’ 1 and Â âˆ’ 1 degrees of freedom. That is, Â is a pivotal quantity, so probability statements such as Â can be answered with the known quantiles of the -distribution. For example, says that P(0.3515 Â = 0.9 when Â = 11 and Â = 16. That is, with 90% confidence.

Suppose Â = 10, Â = 20, sx = 2.3, and sy = 2.8. Find an 80% confidence interval for the ratio of Ïƒx/Ïƒy.

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