Abstract: The change-point model has been proved to have practical significance in many fields, in which the mean single change-point model is the basis of the change-point model. This paper mainly focuses on solving the statistical inference problem of whether there is a change point in a single change-point statistical model. For the mean single change-point model, this paper converts the traditional hypothesis testing idea into an estimation problem for the number of variable points to be 0 or 1, thus avoiding the critical value selection problem; the optimization objective function based on the jump information criterion is established, and the consistency of the number of change points and its convergence speed are proved, and finally the construction form of the optimal jump information criterion is derived. The numerical experimental results show that our proposed method has superior statistical performance compared to existing test-based methods.