Question: A research team took a random sample of 15 observations from a normally distributed random variable Y and observed that \[{{\bar{y}}_{15}}=317.1\] and \[s_{Y}^{2}=326.7\] , where \[{{\bar{y}}_{15}}\] is the average of the fifteen sampled observations and \[s_{Y}^{2}\] is the unbiased estimate of \[\operatorname{var}(Y)\] . A second research team took a random sample of 12 observations from a normally distributed random variable X and observed that \[{{\bar{x}}_{12}}=123.4\] and \[s_{X}^{2}=117.8\] , where \[{{\bar{x}}_{12}}\] is the average of the twelve observations sampled from X and \[s_{X}^{2}\] is the unbiased estimate of \[\operatorname{var}(X)\] . Test the null hypothesis \[{{H}_{0}}:\ \operatorname{var}(X)=\operatorname{var}(Y)\] against the alternative \[{{H}_{1}}:\ \operatorname{var}(X)\ne \operatorname{var}(Y)\] at the 0.01 level of significance. Find a 99% confidence interval for \[\frac{\operatorname{var}(X)}{\operatorname{var}(Y)}\] . Note that an examination question will either ask for the test or the confidence interval.

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