So, this is the question I'm working on:

Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean µ1 and unknown variance σ12. A second random sample from another normal population with unknown mean µ2 and unknown variance σ22 yields the measurements: 13, 7, 9, 15, 11.

b. Use the pivotal method (and a pivotal statistic with F distribution) to derive a 95% confidence interval for σ2/σ1. Work it out for these data. And test the null hypothesis that σ2 = σ1 at the 5% level of significance. [6] (recall that Fv1,v2,a = 1/Fv2,v1,1-a).

So, I'm completely at a loss as to how I can use the pivotal method on the F distribution. Please help me.

So, this is the question I'm working on:

Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $µ_1$ and unknown variance $σ_1^2$. A second random sample from another normal population with unknown mean $µ_2$ and unknown variance $σ_2^2$ yields the measurements: 13, 7, 9, 15, 11.

b. Use the pivotal method (and a pivotal statistic with F distribution) to derive a 95% confidence interval for $σ_2/σ_1$. Work it out for these data. And test the null hypothesis that $σ_2 = σ_1$ at the 5% level of significance. [6] (recall that $F_{\nu_1,\nu_2,a} = 1/F_{\nu_2,\nu_1,1-a}$).

So, I'm completely at a loss as to how I can use the pivotal method on the F distribution. Please help me.