Part BCSIR NET December 2024the-reversed-size-is-one-minus-the-power

The reversed size is one minus the power

Suppose $φ$ is a most powerful test of size 0.05 for testing a simple null hypothesis $H_{0}$ against a simple alternative hypothesis $H_{1}$ . If the power of the test is 0.4, then which of the following is true?

A. $(1 - φ)$ is a most powerful test at level 0.6 for testing $H_{1}$ against $H_{0}$ .✓
B. $(1 - φ)$ is a most powerful test at level 0.4 for testing $H_{1}$ against $H_{0}$ .
C. $(1 - φ)$ is a most powerful test at level 0.05 for testing $H_{1}$ against $H_{0}$ .
D. $(1 - φ)$ is NOT a most powerful test for testing $H_{1}$ against $H_{0}$ at any level.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: A UMP test exists for every testing problem

The reversed size is one minus the power

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