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In spite of the numerous references to problems derived from the incorrect use of the statistical tests or from misinterpretations of their results by experimental researchers in different areas, the educational world has stayed until the moment detached from them. In this paper we present the results of a wide research aiming at carring out a comprehensive evaluation of the learning of the hypothesis test by undergraduates. We point to some difficulties and errors that might underlie the origin of the denounced problems and that the teaching will have to take into account for an improvement of the learning of the topic. Likewise, we describe students' conceptions about two key concepts in statistical test: the logical structure of hypothesis testing and the leve1 of significance.