Consider three tests C1,C2, and C3 of the same hypothesis, performed independently

(e.g., for each of these tests the decision is based on a different sample). Consider now the following three procedures:

A: Reject H0 only if all three tests reject it; otherwise, accept H0, B: Reject H0 only if at least two tests reject it; otherwise, accept H0, C: Reject H0 only if at least one test rejects it; otherwise, accept H0.

(i) Express the power functions of procedures A, B, and C through power functions of tests C1–C3. (ii) Assuming that power functions of tests C1–C3 are the same

(πC1 (θ) = πC2 (θ) = πC3 (θ) = π(θ)), graph the power functions of procedures A, B, and C.