$X$ is distributed by Pareto with
$$f_X (x) = \frac{\alpha k^{\alpha}}{x^ {\alpha +1}},\alpha,k>0,x>k.$$
Derive a 95% confidence interval for $k $.
My friend said I gotta do this
$$Pr (x_{0.025} \leq \frac{k}{\hat k} \leq x_{0.975})= 0.95 \tag {1}$$
Computation-wise is alright because I have found the cumulative density for $k/\hat k $ applied my friends hint and got the confidence interval needed.
However, the rational behind $(1) $ is hard for me to view to find out ir to find the logic. I understand the percentile application but why involve $\hat k $? Why aren't $\alpha$ and $x$ involved?