Give a full and correct answer what is inference concerning the ration of two populations?

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Answer 1

Inference about ratio of 2 variances let the hypotesis be: $H_{0} : \frac{σ_{1} {2}}{σ_{2} {2}} = 1 v s H_{1} : \frac{σ_{1} {2}}{σ_{2} {2}} \neq q_{1}$

$\Rightarrow$ We are testing whethes the two population have same variance of not. This so tested using F-test as we can test $H_{0} : \frac{σ_{1} {2}}{σ_{2} {2}} = 1 v s H_{1} : \frac{σ_{1} {2}}{σ_{2} {2}} > 1$

Here we are testing whethes population 1 has highes variance or not. or we can test

$H_{0} : \frac{σ_{1} {2}}{σ_{2} {2}} = 1 v s H_{1} : \frac{σ_{1} {2}}{σ_{2} {2}} < 1$ Test statistic, we use here is $F = \frac{r \frac{S_{1} {2}}{σ_{1} {2}}}{S_{2} {2}} {σ_{2} {2}}} \sim F_{n_{1} - 1, n_{2} - 1}$ where $S_{i}$ denote sample variance of $i^{t h}$ population $& n_{1}$ , denote sample size of $i^{t h}$ population.

Give a full and correct answer what is inference concerning the ration of two populations?

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