Question: A research team took a random sample of 7 observations from a normally distributed random variable Y and observed that \[{{\bar{y}}_{7}}=789.7\] and \[s_{Y}^{2}=147.3\], where \[{{\bar{y}}_{7}}\] is the average of the seven observations samples from Y and \[s_{Y}^{2}\] is the unbiased estimate of \[\operatorname{var}(Y)\]. A second research team took a random sample of 5 observations from a normally distributed random variable X and observed that \[{{\bar{x}}_{5}}=1073.5\] and \[s_{X}^{2}=2831.3\], where \[{{\bar{x}}_{5}}\] is the average of the five 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 \[{{H}_{1}}:\ \operatorname{var}(X)>\operatorname{var}(Y)\] at the 0.01 level of significance.