What is neyman peason-lemma?

Answer 1

The Neyman-Pearson lemma is a fundamental result in statistical hypothesis testing that provides a method for determining the most powerful test for a given size (type I error rate) when distinguishing between two simple hypotheses. It states that for two simple hypotheses, ( H_0 ) and ( H_1 ), the most powerful test can be constructed by comparing the likelihood ratio of the two hypotheses to a critical value. This lemma is essential for developing optimal tests in various statistical applications, particularly in the context of binary decision-making.