Let X1, ..., Xn be independently normally distributed with means E(Xi) = i and variance 1. The

Let X1, ..., Xn be independently normally distributed with means E(Xi) = µi and variance 1. The test of H : µ1 = ··· = µn = 0 that maximizes the minimum power over ω
:

µi ≥ d rejects when Xi ≥ C.

[If the least favorable distribution assigns probability 1 to a single point, invariance under permutations suggests that this point will be µ1 = ··· = µn =

d/n].