All observable phenomena can be described by alternative mathematical models, which vary in their fidelity and computational cost. Selection of an appropriate model involves a tradeoff between computational cost and representational accuracy. Ubiquitous uncertainty (randomness) in model parameters and forcings, and assimilation of observations of the system states into predictions, complicate the model selection problem. We present a framework for analysis of the impact of data assimilation on cost-constrained model selection. The framework relies on the definitions of cost and accuracy functions in the context of data assimilation for multifidelity models with uncertain (random) coefficients. It contains an estimate of error bounds for a system's state prediction obtained by assimilating data into a model via an ensemble Kalman filter. This estimate is given in terms of model error, sampling error, and data error. Two examples illustrating the applicability of our model selection method are provided. The first example deals with an ordinary differential equation, for which a sequence of lower-fidelity models is constructed by progressively increasing the time step used in its discretization. The second example comprises the viscous Burgers equation as the high-fidelity model and a linear advection-diffusion equation as its low-fidelity counterpart.