Summary: The central idea of the MDL (Minimum Description Length) principle is to represent a class of models (hypotheses) by a universal model capable of imitating the behavior of any model in the class. The principle calls for a model class whose representative assigns the largest probability or density to the observed data. Two examples of universal models for parametric classes \({\mathcal M}\) are the Normalized Maximum Likelihood (NML) model \[ \widehat{f} (x^n\mid {\mathcal M})= f(x^n\mid \widehat{\theta}(x^n)) \biggl/ \int_\Omega f(y^n\mid \widehat{\theta} (y^n)) dy^n, \] where \(\Omega\) is an appropriately selected set, and a mixture \[ f_w(x^n\mid {\mathcal M})= \int f(x^n\mid\theta) w(\theta) d\theta \] as a convex linear functional of the models. In this interpretation a Bayes factor \(B-f_w(x^n\mid {\mathcal M_1})/ f_v(x^n\mid{\mathcal M}_2)\) is the ratio of mixture representatives of two model classes. However, mixtures not be the best representatives, and as will be shown the NML model provides a strictly better test for the mean being zero in the Gaussian cases where the variance is known or taken as a parameter.