I see this question has been posted for a long time, but I'll answer it for you.

The cost for your study would depend on many factors. First and foremost, you would need to decide who your stakeholders will be (who will benefit from this app, and what organizations, groups, etc. would have an interest in this research?). You can then decide on who your subjects will be. The breath and scope of your study would need to be decided on next. An appropriate sample size would then need to be calculated (this is a process in and of itself). After this, you need to decide how best to test your app, and develop a methodology and procedure. Keep in mind that all of this I have mentioned so far would need to be supported by the relevant literature in the field or industry to which your app best applies. If you are doing this study for an institution, you must secure approval to conduct the study from whatever IRB (Institutional Review Board) your institution uses (This means you will have to write a proposal of some form). You are now ready to calculate what your study will (or should) actually cost! From there, you can search and apply for grants to secure the funds for your study. Grants is a whole other topic! Let me know if I can help. Good luck!