In the implementation of a linear regression model, it is crucial to carry out significance tests to assure the proper inclusion of parameters. In addition, in order to perform such a hypothesis test, students should verify the properties of the residuals and the most important is undoubtedly the normality of the residuals. However, it is clear that there is, in general, an important gap between the hypothesis testing and residuals verification stages. In this paper we present an empirical study about the most probable confusions and misunderstandings students have in relating these two mental statistical constructs in a course of Administrative Statistics in a Mexican Education Higher Institute. One of the main results is that the order in which these two concepts are taught is essential to guarantee there is not a disconnection between the two stages, and perhaps it would be better to first analyze the properties of the residuals and then to engage in the hypothesis testing phase.