Training machine learning models to identify human behavior is a difficult yet essential task to develop autonomous and adaptive systems such as smart homes. These models require large and diversified amounts of labeled data to be trained effectively. Due to the high variety of home environments and occupant behaviors, collecting datasets that are representative of all possible homes is a major challenge. In addition, privacy and cost are major hurdles to collect real home data. To avoid these difficulties, one solution consists of training these models using purely synthetic data, which can be generated through the simulation of home and their occupants. Two challenges arise from this approach: designing a methodology with a simulation able to generate credible simulated data and evaluating this credibility. In this paper, we explain the methodology used to generate diversified synthetic data of daily activities, through the combination of an agent model to simulate an occupant, and a simulated 3D house enriched with sensors and effectors to produce such data. We demonstrate the credibility of the generated synthetic data by comparing their efficacy for training human context understanding models against the efficacy generated by real data. To achieve this, we replicate a real dataset collection setting with our smart home simulator. The occupant is replaced by an autonomous agent following the same experimental protocol used for the real dataset collection. This agent is a BDI-based model enhanced with a scheduler designed to offer a balance between control and autonomy. This balance is useful in synthetic data generation since strong constraints can be imposed on the agent to simulate desired situations while allowing autonomous behaviors outside these constraints to generate diversified data. In our case, the constraints are those imposed during the real dataset collection that we want to replicate. The simulated sensors and effectors were configured to react to the agent's behaviors similarly to the real ones. We experimentally show that data generated from this simulation is valuable for two human context understanding tasks: current human activity recognition and future human activity prediction. In particular, we show that models trained solely with simulated data can give reasonable predictions about real situations occurring in the original dataset. We also report experimental results regarding statistical analysis and C2ST to assess the credibility of generated data. We discuss the generality of our approach for evaluating the credibility of simulated data from their use as training data.