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

Let X1, …, Xn be independent and 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].