In some engineering applications, such as chaotic encryption, chaotic maps have to exhibit required spectral and statistical properties close to those of random signals. In order to evaluate the latter features, statistical tests developed for random number generators (RNG) can also be applied to chaotic maps, in order to gather evidence that the map generates ”good” chaotic signals, i.e. having a considerable degree of randomness. To address this particular problem, different statistical tests for the systematic evaluation of the randomness of cryptographic random number generators can be applied, among which the most popular NIST (National Institute of Standards and Technology) tests. In this paper we present the analysis of a new ultra weakly coupled maps system introduced by Lozi (its statistical properties and its evolution with parameter variation.