Hypothesis Testing Instrument

Neyman-Pearson
Lab

Most powerful, UMP, and UMPU test derivation, built live from the Neyman-Pearson lemma - with the full proof, the test function, and the critical region.

9 distributions · exact derivations · live critical regions

Interactive Lab

Find the most powerful test.

Choose a distribution and hypotheses. The Neyman-Pearson lemma, the Karlin-Rubin theorem, and the unbiasedness condition construct the optimal rejection region live.

Scope. Exact for nine one-parameter families with closed-form sampling distributions. Two-sided UMPU is solved numerically for continuous families; discrete two-sided tests are flagged.

Distribution

Distribution family

Parameter under test

Sample

Sample size n

Hypotheses

θ₀

Null H₀

Alternative H₁

Significance

0.050 α (Type I error)

0.01 0.05 0.10 0.15 0.20 0.25

Neyman-Pearson
Lab

Find the most powerful test.

Distribution

Sample

Hypotheses

Significance

Derivation

Test function

Sampling distribution & critical region

Neyman-PearsonLab

Distribution

Sample

Hypotheses

Significance

Derivation

Test function

Sampling distribution & critical region

Neyman-Pearson
Lab