(Solution) - A Find the 1 confidence set for a -(2025 Original AI-Free Solution)

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a. Find the 1 - ? confidence set for a that is obtained by inverting the LRT of H0: ? = a0 versus H1: a ? a0 based on a sample X1,..., Xn from a n(?, a?) family, where ? is unknown.
b. A similar question can be asked about the related family, the n(?, a?2) family. If X1,..., Xn are iid n(?, a?2), where ? is unknown, find the 1 - ? confidence set based on inverting the LRT of H0: a = a0 versus H1: a ? a0.