We take a Student process that is based on independent copies of a random variable X and has trajectories in the function space D[0,1]. As a consequence of a functional central limit theorem for this process, with X in the domain of attraction of the normal law, we consider convergence in distribution of several functionals of this process and derive respective asymptotic confidence intervals for the mean of X. We explore the expected lengths and finite-sample coverage probabilities of these confidence intervals and the one obtained from the asymptotic normality of the Student t-statistic, thus concluding some alternatives to the latter confidence interval that are shorter and/or have at least as high coverage probabilities.