Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method

This article presents procedures for hypothesis testing and interval estimation of the common mean of several normal populations. The methods are based on the concepts of generalized p-value and generalized confidence limit. The merits of the proposed methods are evaluated numerically and compared with those of the existing methods. Numerical studies show that the new procedures are accurate and perform better than the existing methods when the sample sizes are moderate and the number of populations is four or less. If the number of populations is five or more, then the generalized variable method performs much better than the existing methods regardless of the sample sizes. The generalized variable method and other existing methods are illustrated using two examples.