Recent approaches to statistics education situate the teaching and learning of statistics within cycles of statistical inquiry. Learners pose questions, plan, and collect, represent, analyse and interpret data. We focus on the first step -- posing statistical questions. Posing statistical questions is a critical step as questions inform the types of data collected, determine the representations used, and influence the interpretations that can be made. We report on an investigation of 158 prospective elementary teachers as they design statistical questions to support group comparisons. Support was provided through implementation of three phases of question development (think, peer-feedback, and expert-feedback). We describe the features of initial statistical questions posed, examine refinements made to statistical questions, and evaluate the effectiveness of both peer and expert feedback. Our study reveals that generating adequate statistical questions is particularly complex and requires considerable time, targeted feedback, and support. With appropriate support, in the form of peer and expert feedback provided within a three-phase question design scenario, prospective elementary teachers could generate adequate statistical questions suitable for use in primary classrooms. While this study provides compelling evidence to support the use of expert feedback, further research is required to identify the best ways to support prospective teachers in both providing and implementing peer-feedback.