Suppose that \(X_{1}, \ldots, X_{n}\) is a set of independent and identically distributed random variables from a distribution \(F\) with parameter \(\theta\). Suppose that \(F\) and \(\theta\) fall within the smooth function model. For the case when \(\sigma\) is known, prove that \(\tilde{\theta}_{n, \text { ord }}\) is a first-order correct and accurate \(100 \alpha \%\) confidence limit for \(\theta\).