A New Testing Procedure with A Random Alternative on Hypothesis Testing

摘要

One needs to make a choice among two mutually exclusive claims on the traditional hypothesis test. In the paper, a generalization to random alternative hypothesis is proposed. The fundamental difference with the traditional hypothesis test is that the new alternative hypothesis is a partition of m multiple claims and is data-dependent. Data is used to decide which claim in the partition to be tested as the alternative. As an application of our proposed, the one-sample problem is provided. In consequence, the famous two-sided t-test should be replaced by the proposed.