Under the assumptions of Problem 10.1, determine the most accurate invariant (under the transformation X
= −X) confidence sets S(X)

with P(ξ ∈ S(X) | E) + P(ξ ∈ S(X) | F)=2γ.

Find examples in which the conditional confidence coefficients γ0 given E and γ1 given F satisfy

(i) γ0 < γ1; (ii) γ0 > γ1.