Abstract Let x = (x 1 ..., x n)′ be an n-dimensional normally distributed stochastic vector with mean m = (m 1 ..., m n)′ belonging to a subspace M of Rn and with covariance matrix C. It is well known how to obtain simultaneous confidence intervals for a class of linear functionals of the mean in different contexts. An early paper is Working and Hotelling [11]. More recent papers are Hoel.