Since computers have become increasingly more powerful, users are less willing to accept slow responses of systems. Hence, performance testing is important for interactive systems. However, it is still challenging to test if a system provides acceptable performance or can satisfy certain response-time limits, especially for different usage scenarios. On the one hand, there are performance-testing techniques that require numerous costly tests of the system. On the other hand, model-based performance analysis methods have a doubtful model quality. Hence, we propose a combined method to mitigate these issues. We learn response-time distributions from test data in order to augment existing behavioral models with timing aspects. Then, we perform statistical model checking with the resulting model for a performance prediction. Finally, we test the accuracy of our prediction with hypotheses testing of the real system. Our method is implemented with a property-based testing tool with integrated statistical model checking algorithms. We demonstrate the feasibility of our techniques in an industrial case study with a web-service application.