Hypothesis Test

ProbabilityTheoryStatistics Given two disjoint sets of the parameter space , we have two competing hypotheses: We call the null hypothesis which is typically the setting of parameters that assume are true and want to conduct statistical tests in order to provide evidence against. In other words, we want to construct a statistic such that on any data with high when . A test can be specified by any rejection region which indicates the collection of all settings of the parameters giving evidence against the null hypothesis .