I discourage "book report" type projects, but well-written accounts of research literature are appropriate, such as Infant mortality rate (Jennifer Cheng and Wing Tam) written in the style of the Ropeik-Gray Risk book.
Repeating experiments dealing with the psychology of probability is fun: Risk aversion in games of chance (Rose Cendak and Rebecca Graff) shows how people can calculate probabilities rationally while simultaneously believing in lucky/unlucky streaks.
Sports data provides an endless range of possible projects. Strategies in fantasy NBA basketball (Tommy Lu and Angela Zhang) devise improved player-ranking schemes for managers of fantasy basketball to plan advantageous drafts and trades; they modestly didn't say that they won their league competition. In an honors thesis project parallel to the course, A regression model using common baseball statistics to project offensive and defensive efficiency (Dennis Moy) studies improved ways of using runs scored and runs allowed to predict winning percentages.
During the course I point out uses of simulation to study models too complicated for theoretical analysis. The evolution of cooperation:the spatial public goods game (Itamar Landau) gives a simulation study of a spatial nonzero-sum game.
Stock market behavior is another focus of the course. Time-variant CAPM: learning about factor loading (Jiho Han) describes a variant of recent sophisticated models and assesses its realism.