We propose a test of a qualitative hypothesis on the mean of a n-Gaussian
vector. The testing procedure is available when the variance of the
observations is unknown and does not depend on any prior information on
the alternative. The properties of the test are non-asymptotic. For
testing positivity or monotonicity, we
establish separation rates with respect to the Euclidean distance, over
subsets of $\mathbb{R}^{n}$ which are
related to Hölderian balls in functional
spaces. We provide a simulation study in order to evaluate the
procedure when the purpose is to test monotonicity in a functional
regression model and to check the robustness of the procedure to
non-Gaussian errors.