The Poisson distribution is here used to illustrate Bayesian inference concepts with the ultimate goal to construct credible intervals for a mean. The evaluation of the resulting intervals is in terms of potential negative effects of mismatched priors and posteriors. The discussion is in the form of an imaginary dialogue between a teacher and a student, who have met earlier, discussing and evaluating the Wald and score confidence intervals, as well as confidence intervals based on transformation and bootstrap techniques. From the perspective of the student the learning process is akin to a real research situation. By this time the student  is supposed to have studied mathematical statistics for at least two semesters.