The Neyman-Pearson lemma is a fundamental principle in statistical hypothesis testing. It provides a method for determining the most powerful test for a given significance level when comparing two hypotheses: the null hypothesis and the alternative hypothesis. The lemma states that the likelihood ratio test is optimal, meaning it maximizes the probability of correctly rejecting the null hypothesis while controlling the probability of a false positive. In practical terms, the lemma helps researchers decide which test to use when they want to distinguish between two competing hypotheses. By focusing on the likelihood ratio, it ensures that the chosen test is the most effective in detecting true effects while minimizing errors.