In this paper we consider the problem of inference from accelerated life tests in which a common parametric family of life distributions at the different stress levels is not specified in advance. By assuming a time transformation function, which is a version of the familiar inverse power law, we give a procedure for testing hypotheses that the unknown distributions are specified members of a location-scale family. The behavior of the test procedure is indicated by some simulations. We illustrate the methodology with some real-life data.