The decision in the Bayesian hypothesis testing depends on the posterior probability distribution of the associated parameter and the loss function. In turn, the posterior probability distribution depends on the prior probability distribution of the parameter. Goal programming is used in this paper to study the robustness of the decision to the changes in the posterior probability and\or the loss function. The approach depends on the fact the hypothesis-testing problem can be reformulated in the language of a single stage decision theory. Three types of sensitivity analysis are considered in the paper; sensitivity analysis for the posterior (prior) probabilities keeping the loss function fixed, sensitivity analysis on the loss function keeping the probabilities fixed and sensitivity analysis on both the probabilities and the losses. The bounds of changes in the probability and\or the losses are determined by using the linear goal programming in the first and second case. For the joint sensitivity on both the probabilities and the losses, the problem is converted to a multiobjective program then to a nonlinear goal program. By using the suggested approach, the global optimal solution is attained in the first and second cases because of using linear goal programs. The nonlinearity in the third case can be managed by the priority ranking in the achievement function.