On the use of inferential confidence intervals

Inferential confidence intervals (CI) represent a widely used technique for testing the equality of the means of two Normal distributions by comparing two particular CI’s relative to the each mean. They allow simple graphic interpretations and result as being more informative than the traditional testing technique through the confidence levels. Yet they are unable to convey the information relative to the compatibility of the null hypothesis with the observed data usually provided by the p-value. The present paper identifies a new measure of such compatibility in the context of inferential CI’s and extends the technique to the non Normal case. Moreover, in case the null hypothesis is accepted, the problem of estimating the common mean is dealt with by means of the bounds of specific inferential CI’s. The proposed procedures are then applied to real data relative to foreign populations originating outside the European Union and sampled from the Italian territory.