Likelihood Ratio Tests for Interval Hypotheses with Applications

Abstract

In this article, we derive the likelihood ratio tests (LRTs) for simultaneously testing interval hypotheses for normal means with known and unknown variances, and also with unknown but equal variance. Special cases when the interval hypotheses boil down to a point hypothesis are also discussed. Remarks regarding comparison of the LRT with tests based on combination of p-values are made, and several applications based on real data are mentioned.

Keywords:

• Asymptotic normality
• Fisher’s z transformation
• Interval hypotheses
• Likelihood ratio test
• Lyapounov condition
• p-values

Mathematics Subject Classification:

• Primary 62H15; Secondary 62H03