Return to the situation described in Example 9.1.7. Consider a different test that rejects H0 if Yn 2.9 or Yn 4.5. Let

Return to the situation described in Example 9.1.7. Consider a different test δ∗ that rejects H0 if Yn ≤ 2.9 or Yn ≥ 4.5. Let δ be the test described in Example 9.1.7.
a. Prove that π(θ|δ∗) = π(θ|δ) for all θ ≤ 4.
b. Prove that π(θ|δ∗) < π(θ|δ) for all θ >4.
c. Which of the two tests seems better for testing the hypotheses (9.1.8)?