Let 1, 2,. . .,n and1,2,. . .,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  is known to be the -distribution with  − 1 and  − 1 degrees of freedom. That is,  is a pivotal quantity, so probability statements such as  can be answered with the known quantiles of the -distribution. For example,

says that P(0.3515  = 0.9 when  = 11 and  = 16. That is,

with 90% confidence.

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

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