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(, a2) family If X1, , Xn are iid n(, a2), where is unknown, find the 1 ...

These densities have already appeared in Exercise 88 where LRT ...

a. Find the 1 - confidence set for a that is obtained by inverting the LRT

Question:

a. Find the 1 - α confidence set for a that is obtained by inverting the LRT of H0: α = a0 versus H1: a ≠ a0 based on a sample X1,..., Xn from a n(θ, aθ) family, where θ is unknown.
b. A similar question can be asked about the related family, the n(θ, aθ2) family. If X1,..., Xn are iid n(θ, aθ2), where θ is unknown, find the 1 - α confidence set based on inverting the LRT of H0: a = a0 versus H1: a ≠ a0.