In this paper, Bayesian life test sampling plans are developed for the Weibull distribution with known shape parameter under type I censoring. Specifically, we consider the choice of the truncation time t_o and the sample size n which maximize the expected gain in information under a certain cost constraint. This measure of information is appropriate when the objective is to gain knowledge about a certain parameter or a future observation. We mainly restrict our attention to deal with information about the scale parameter of the distribution and any-one-to-one transformation of it. The exact evaluation of the expression of information and the corresponding optimal design is obtained numerically. Approximate expressions for the expected gain in information are suggested and used to derive some analytical results for the optimal design. Numerical results are provided to check the accuracy of the approximate results. A related problem where information is required about the minimum lifetime of a future experiment is also discussed.