The notions of statistical hypothesis and statistical test. Type I error, Type II error, power of a test. Relation between tests and confidence intervals. Fundamental Lemma of Neyman-Pearson. Uniformly most powerful (UMP) tests. Monotone likelihood ratio property and UMP test for one parameter exponential families. Applications to normal populations, z-test, t-test, chi-square test, F-test; p value. Generalized likelihood ratio tests. Chi-square goodness of fit test, contingency tables. Kolmogorov-Smirnov test. Bayes tests, minimax tests.