solution

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, s_x= 2.3, and s_y = 2.8. Find an 80% confidence interval for the ratio of σ_x/σ_y.