Profile evaluation for Statistics PhD

[stats07]

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 university
Major(s): Mathematics
GPA in Major: 4.0
Overall GPA: 3.98

GRE 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 award

Pertinent Activities or Jobs: 3 years experience as TA and Supplemental Course Instructor for Mathematics department, 8 years private tutoring experience

Letters 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++

[ace589]

Your GRE and GPA are awesome.  I'm assuming that you took a few other math corse courses as well?  

The TA experience could be influential as well.  What area in the social sciences do you most enjoy?  You may apply to those programs as well.  Most social sciences will have quantitative methods specializations.  There are many more of these programs than stats programs with a concentration.  Viewing the roster most of them will have undergraduate or masters degrees in mathematics.

Edited September 16, 2015 by ace589