Since graduate student statisticians receive a letter grade for the course, suitable projects are those where the majority of the work could be completed in a 5 week period.  For example, the statistician should be able to learn the background material of the project, define the scientific goals, select the statistical methodologies to achieve the scientific goals, analyze the data to obtain results and relevant graphics, write a preliminary draft of a publishable manuscript, and present the major findings by the end of the quarter; the actual submission of the manuscript and response to reviewers could be done after the quarter.  Another scenario might not involve data directly but where a substantial amount of statistical work is needed prior to data collection; this might take the form of a grant proposal.