Inferential reasoning is an integral part of science and civic society, but research shows that it is a problematic domain for many people. One possibility for a more accessible approach to inferential reasoning is to use randomization tests via computer simulations. A case study was conducted with primary preservice teachers after they had passed a course module that introduced inferential reasoning with randomization tests. The study examines how three pairs of primary preservice teachers construct models in a randomization test task with both hands-on and computer-supported components. Our findings suggest that there is a common sequence in the model building process: planning, modeling the random assignment, setting sample size and replacement, and running the simulation. Our findings show in depth how TinkerPlots can be a supportive and constraining medium in the modeling process, building on experiences with physical simulations of a randomization test. These insights can be used for redesigning technology-supported learning trajectories for randomization tests. Together with other case studies our findings provide a good sense of university students' modeling processes.