Part CCSIR NET December 2024the-upper-tail-costs-no-size

The upper tail costs no size

Let $X_{1}, X_{2}, X_{3}$ be a random sample from Uniform $[0, θ]$ distribution, $θ > 0$ . Consider the likelihood ratio test of size 0.001 for testing $H_{0} : θ = 3$ against $H_{1} : θ \neq = 3$ . Then, which of the following statements are true?

A.If max{ $X_{1}, X_{2}, X_{3}$ } is 3.1, then $H_{0}$ is rejected.✓
B.If max{ $X_{1}, X_{2}, X_{3}$ } is 1.3, then $H_{0}$ is rejected.
C.If max{ $X_{1}, X_{2}, X_{3}$ } is 0.1, then $H_{0}$ is rejected.✓
D.The power of the test at $θ = 0.3$ is 1.✓

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.

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50 are analysed free — try those first.

The upper tail costs no size

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