# Understanding the Concepts and Skills Give correct answer for in using F-procedures to make inferences for two population standard deviations, why should the distributions (one for each population) of the variable under consideration be normally distributed or nearly so?

Understanding the Concepts and Skills Give correct answer for in using F-procedures to make inferences for two population standard deviations, why should the distributions (one for each population) of the variable under consideration be normally distributed or nearly so?
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Szeteib

By the definition of F — distribution we have $F=\frac{\frac{X}{{V}_{1}}}{\frac{Y}{{V}_{2}}}$ Where $\begin{array}{|ccc|}\hline X& \text{&}& Y\\ \hline\end{array}$ are two independent chi-square variates with ${V}_{1}$ and ${V}_{2}$ degrees of freedom Now for a ${\chi }^{2}$ - variate is a very necessary to assume that the variable under consideration is a normal variate because the ${\chi }^{2}$ -variate is defined as the square of standard normal variate. Therefore for the F-procedures to make inferences for two population standard deviations. The distributions (one for each population) of the variable under consideration is normally distributed or nearly so.