For the location scale model in Problem 13.45, show that, for testing 0 versus

For the location scale model in Problem 13.45, show that, for testing µ ≤ 0 versus µ > 0, argue that the Wald test is LAUMP if β ≥ 1. If ˆσn is replaced by any consistent estimator of σ, does the LAUMP property continue to hold? If 1/2 <β< 1, argue that the Rao test is LAUMP.