In a question it is asked to compute the estimator $\frac{\hat{\sigma}^2}{\sigma^2}$ and thus compute the confidence interval for a given set of data. I've already found the maximum likelihood estimator $\hat{\sigma}$ but I'm confused here as I dont understand the difference between $\hat{\sigma}$ and $\sigma$ and also what $\frac{\hat{\sigma}^2}{\sigma^2}$ represents. Also the probability function is a log normal distribution of $f(x) = \frac{1}{x\sigma\sqrt{2\pi}}e^{-\frac{ln(x)^2}{2\sigma^2}}$
I've found $\hat{\sigma} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{\ln{x_i}}}$
All the question provided was the pdf.