Hi all, I'm a senior at a top 50-ish public university, pretty well known, will be graduating this spring, and am planning on applying to statistics grad programs starting Fall of 2019 (i.e. to start in Fall 2020). I'm majoring in Applied Math but have a lot of statistics coursework (taken pretty much all possible probability/stats courses offered in the department), including mathematical statistics, computational statistics(using R), and a data analysis course. I have gotten A's or A-'s in all these courses. I have also taken graduate level Applied Statistics 1 and 2, getting a B+ and A+ respectively, and am currently taking a graduate level course in Survival Analysis, which I expect to do quite well in. I've also taken a basic course sequence in real analysis, as well as courses in probability involving stochastic processes. My GPA overall is 3.75. While I have yet to take the GRE, I'm fairly confident I can do well, and overall I think my academics, while not incredible, are decent.
My real issue comes from the fact that I don't really have much relevant experience with respect to research or internships. I will be working in a full-time data analyst position starting this summer, but other than that I have essentially nothing.
I do believe that I can get strong letters of recommendation, because I have gotten to know some of my professors pretty well, and have done well in their classes.
With this in mind, is it realistic for me to directly apply for PhD programs in Statistics? Or would it be more beneficial to me to do a Masters program first (one with a research requirement, obviously) and then apply for PhD programs after that?
Would really appreciate any advice! Thanks