If there exists a critical region 
of size 
and a nonnegative constant
such that
 |
for points in 
and
 |
for points not in 
,
then 
is a best critical region of size 
.
Neyman-Pearson Lemma
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References
Hoel, P. G.; Port, S. C.; and Stone, C. J. "Testing Hypotheses." Ch. 3 in Introduction to Statistical Theory. New York: Houghton Mifflin, pp. 56-67, 1971.Referenced on Wolfram|Alpha
Neyman-Pearson LemmaCite this as:
Weisstein, Eric W. "Neyman-Pearson Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Neyman-PearsonLemma.html