This paper emphasizes on the correction of a misconception among the students about the presence of negative dead time values determined by using a two-source method. To specify the importance of this work, weak sources have been designed specifically so that broad distribution of dead time values can be obtained including 30-40% of the negative values. During the measurements, students usually eliminate the measured negative dead time data intuitively, which leads to an inaccurate average detector dead time. In this work, together with the experimental results from the two-source method, we also performed Monte Carlo simulation. Thus, we correlated the statistical average distribution of dead time and proved that negative value of dead time exists when the weak sources are applied. Furthermore, these negative dead time values play a crucial role in determining the accurate dead time. Thus, this work will serve to be an excellent model for the students to learn about the scientific discipline in handling the experimental data correctly and the importance of error propagation in counting statistics.