A Simple Asymptotic Bound on the Error of the Ordinary Normal Approximation to the Student´s t-Distribution

A simple asymptotic bound on the error of the ordinary normal approximation (ONA) to the Student´s t-distribution is derived. The proposed bound provides a quick calculation of the minimum number of degrees of freedom required to ensure a given approximation error. Then, the application of the ONA is investigated in confidence interval determination and detection theory. Finally, using the proposed bound, further simple bounds on the approximation error of the confidence level and the false-alarm probability are obtained.