I'm applying to Statistics PhD programs and would love some feedback about whether or not the schools on my list are too selective for my profile. Due to research interests, I am looking for a program that either has a concentration for the social sciences, is conducive to interdisciplinary research, allows for some flexibility in coursework to tailor to specific interests, and/or has faculty with interests in the applications to the social sciences. So far the list I've come up with is U of Washington, Duke, North Carolina, U of Illinois, U of Michigan, and Northwestern U. However, most/all of these seem to have very low acceptance rates. Based on my profile, should I be applying to "safer" schools that may not be as good of a fit for my research interests? My profile is as follows: Undergrad Institution: small liberal arts universityMajor(s): MathematicsGPA in Major: 4.0Overall GPA: 3.98GRE Scores (revised version):Q: 166 (92%)V: 159 (81%)AW: 4.0 (56%)Research Experience: Completed a capstone thesis as a part of the University Honors program, where statistical analysis was the basis of the research. Held two summer internships and now a job as research assistant/analyst. Didn't get in depth statistical analysis experience through these but did get exposure to database management, data modeling, survey methodology, etc. Awards/Honors/Recognitions: summa cum laude, recipient of top mathematics departmental awardPertinent Activities or Jobs: 3 years experience as TA and Supplemental Course Instructor for Mathematics department, 8 years private tutoring experienceLetters of Recommendation: have 3 professors in the mathematics department who know me well and will speak highly of me, but all come from my small school Stats Courses taken: Probability and Statistics, Mathematical Statistics (Calc based), Regression and Time Series (all using SPSS) Proof-based courses: Real Analysis, Abstract Algebra, Mathematical Statistics (same as above), Number Theory, Discrete Other courses: Linear Algebra, Numerical Analysis (MATLAB) I received As in all of the courses listed above. Also have advanced knowledge in Excel, some exposure to C++