I have a sample of experimentally observed data and a parametric distribution model which is expected to explain the data. I estimated the model parameters by the maximum likelihood. Now I need to test whether the sample mean does not significantly differ from the 'theoretical' mean predicted by the model.
The naive approach is to compute the 'theoretical' mean and perform a one-sample t-test. But this approach seems flawed because the model was estimated from the same sample, hence the 'theoretical' mean actually depends on the data.
What techniques may be appropriate for the task, and what theory lies behind this formulation? This question seems similar, but it doesn't have a definite answer.