For simple hypotheses (H_0:\theta=\theta_0) vs. (H_1:\theta=\theta_1), the most powerful test at level (\alpha) rejects when the [ \Lambda(x) = \fracL(\theta_0;x)L(\theta_1;x) ] is less than a threshold (k_\alpha). This lemma underlies many standard tests (e.g., z‑test, t‑test).
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