Robbentheking

I think perhaps you're being a bit myopic based on your own very limited experiences and slightly rude. If a person enters a program in a new city which requires he or she put in 60-70 hrs a week to excel, it's very possible the person will find it difficult to meet people outside the program or have the time to build a relationship with them. If you didn't have time to play rugby, what types of friends would that leave you with?

I am in a similar boat. But I did something different from what you did. I just honestly tell them where I am from, and more importantly let them know I am proletarian. I guess when you are more openly talk about your problems in a sincere way, there are generally two types of people: 1. those who are quickly tired of your stories and problems 2. those who are interested in listening and/or willing to help if possible. You can quickly identify who may be more suitable for you to continue to hang out more often and know more about each other in this way. 
You willed to loan the money to your family rather than spending that money in buying things for yourself. This means that you exercised your free will to take this action to help your sister, giving priority to help others in stead of yourself. This is a case of altruism. I guess your essential problem is not that you do not have the money to buy the things you window shopped. You did have the money. If you had not had loaned the money to your family, you could have used that money to buy the things you window shopped. The essential issue here is that you gave priority to the happiness of your family rather than to your own pleasure. That was your choice. But now you somehow regret your choice because as a result of your altruism to your family you cannot enjoy the shopping that you could have enjoyed. How to solve this problem? Well, switch your priority if you can will to do so. 
You may say you have the moral obligation to help your sister out. But honestly speaking, not matter from Aristotelian ethics (reason over emotion) , deontological ethics (rationality as basis of morality), utilitarianism (maximization of utility), contractualism/contractarianism (mutual agreement), it is hard to justify that it is morally required to give priority to your family over yourself, unless you are simply altruistic, and choose to exercise your free will to help at the cost of your own happiness. For example, you said that you parents did not support you for your college career in a substantial sense. Then, ask yourself why you should support them for the EFC that they are supposed to contribute, and why you should take the responsibility of theirs. Is there any social contract going on here? If so, what kind of social contract? If no social contract at all, isn't it unfair to even ask you to contribute, regardless of whether you are opulent or are eking out a living? 
Based on your description, I also feel that your family members are trying to take advantage of (i.e. exploit) you. They did not financially support you for many years yet ask you for financial support for their own problems. Isn't this a text-book definition of exploitation (i.e. giving out little and then demanding a lot back)? Given that you are now self-supported and can make a living with your stipend, AND given that your family can barely support you for anything, it may be better for you to distance yourself from your family, or simply quit from it and cut whatever ties you may have with them. After all, a family is not unlike other social institutions such as a school, a company, etc, and you should have the right to quit if you are treated unfairly in such a social institution. A detailed discussion of family as a social institution can be found in this book: The Origin of the Family, Private Property, and the State (published in 1884). So, if you have time, take a look at this book, and you will have a better idea what family is all about. 
 
 
 
 
 
 

If you think the application process is too tedious and boring, you may not be cut out for pursuing a PhD, to be blunt.

@TakeruK
Well, I may be deemphaisizing research a bit on some subscious level just as an ego boost, but what I've written above is a pretty decent respresentation of what I've heard in my math department.
With regards to the mathematical ceiling, I think it can really have a more dynamic definition. Math can get really hard and no matter who you are, you are going to get to points where you just really need to like math enough to put in the time and grind through the rough patch. The degree to which you are willing to sacrifice for the subject is part of your ceiling I think, and I think most professors would agree to that. Mathematical ceiling is a phrase that is casually thrown around a lot that is actually pretty deep imo.
In general, I'm wary of people who fall cleanly on either  side of the fixed intelligence vs. growth mindset debate. I think experience shapes all of his greatly on everything from aparent ability to desire to learn something, but the idea that there aren't people with inherent advantages in certain areas doesn't make much sense to me. Forgive me if I sound really stupid because I'm reaching far out of my field, but I'm not sure I understand how humans fit into the evolutionary framework if intelligence is just something we all acquire during our lifetimes.

HAHAHAHA oh this  is a funny troll

You can't just decide you want to get your doctorate in anything just because it sounds cool to have one.  You need to have passion for whatever you are doing, not just doing it because it gets you out of waiting tables.  A ED pointed out, you can wait tables just as easily with a doctorate degree.  You need to build marketable skills.  School is only one way of doing that, and if you don't do school right, you won't build them there.
That being said, you should check out some business programs.  Finance, risk management, and accounting all rely heavily on Economics for their theory.

Or that if Sarah has been manipulating results to produce negatives, who says she isn't doing the opposite too? And that would blow back on the professor.
When you have time and space, I would encourage you to reflect on how you handled this politically. My read is: not particularly well. Not that you should have - this isn't something we're trained explicitly for. But remember the lessons going forward.

cyberwulf, I'm not sure I would hold up a perfect GPA as the standard for a stats applicant to be considered uber-competitive and in the peer group with aridneptune, but let's say something like >3.9 within math (with lots of courses), and not much lower overall from the kinds of schools you've heard of. Without weird weightings, that essentially means over 3/4 of math grades are A's and the remainder are A-'s, which sounds like a reasonable peer group to me. Given that, I'm quibbling with your quibble (instead of working on my research ) and think you're underestimating how many stats applicants are out there with comparable profiles.
 
I had a job some years back analyzing data for a consortium of 30-odd highly ranked private colleges, more or less the same ones that are vastly overrepresented among baccalaureate institutions in PhD programs. One of the fun facts I learned was that at pretty much all of these schools, math majors disproportionately had very high GPAs. My undergrad is a typical example: over one-third of math majors in my year graduated in the top 5% of students (>3.9 overall). Nearly all the rest were still in the top 25% of students (>3.7 overall, almost certainly higher in major). When I used to do resume review and interviewing in my old job, too, we looked for econ or math majors with high grades in statistics/econometrics classes mostly from fancy schmancy schools like Dartmouth and Wesleyan. There, too, I encountered a surprising number of students with very strong math backgrounds and grades. 3.9s in math, apparently not rare at all and not limited to those with math or econ PhD aspirations! Not certain why, but my observation is that a lot of students won't touch non-required math unless they've already gotten a lot of A's in the lower level courses. By this selection mechanism, then students who continue taking mostly math (and related classes in CS, econ, physics, or logic) will continue to get mostly A's and A-'s, especially since upper-level classes rarely curve.
  So sure, the best math majors mostly go to pure math PhDs, I wouldn't dispute that. But because of the high concentration of near-perfect grades among math majors, at most good schools there will still be at least one math-ish major (current or someone who graduated in the past few years) who meets the high grade standards in my first paragraph and is applying to statistics or biostatistics programs. In the aggregated stats applicant pool, count on at minimum a dozen strong applicants from LACs like Pomona, Swarthmore, Amherst, Carleton, Williams, a bunch more -- even little ol' St. Olaf is a powerhouse. I think I'm underestimating the LAC contingent actually. Then count on a couple dozen more applicants from the mega name-brand research universities (Stanford's programs alone must send out a half dozen people at a time and I think Chicago too). Throw in another couple dozen apps from other respected schools like UNC. Basically, name all the good private and public schools you can, and imagine that there's on average one current senior or recent grad with strong credentials applying to stats departments (because, again, high grades are not at all unusual for math majors). And surely most of the recommendations for this crowd are quite good, especially for the substantial portion of these applicants coming from small schools who get detailed personalized recs or those with access to bigger names?   Anyway, a couple dozen here and there ballparks to something like 60 applicants in the pool who are going to be at the top of the piles everywhere they apply, so I think a fair number more than what you have in mind. It would be a big pain, but you could look up profiles of first-year grad students at the top 15 or so statistics departments, and I bet you would find enough students who majored in something math-ish graduating with high honors (proxy for high GPA) at a well-reputed undergrad to substantiate my claim. In my cohort alone there are at least 6 of us who would meet that description, have to imagine the scene is similar elsewhere.

For what it's worth, I was admitted to three schools that "highly recommend" the math GRE without submitting it (Chicago, Washington and Columbia), as well as Berkeley. I got ~70% and only submitted it to Stanford (where I did not get in), based on the recommendation of my undergrad research adviser. I also had a very strong math background which probably earned me the benefit of the doubt - multiple graduate level measure theory courses with all A+s, and a letter from a prof I spent a summer with doing research in abstract analysis. You can probably find my profile somewhere online if you want more context.

Admission statistics doesn't mean anything if you don't know who is in the pool
If my memory didn't go wrong, in 2012 Stanford admitted 20 students out of 120, which is far more than 5%.

Since this thread has been revived, may as well follow up for future statistics PhD applicants who wondering what to do about the subject test. (n=1, though, people, n=1.) I had a 58%ile subject score. I submitted it to Chicago and got in. I did not submit it to Berkeley, Columbia, Duke, IA State, Michigan, Northwestern, or Washington but still got in. I did not submit it to CMU or Harvard and did not get in. I'm guessing that the presence/absence of that subject test score had little bearing on any of these results.

I always thought the bigger bias would be that people who were accepted were more likely to post their results

Well, I'm not saying that having an advanced degree hurts. My experience has been that connections predominate everything else in terms of getting hired. And if a group's managing director went to NYU Stern and you've got an NYU MFE Master's you'll be looked kindly upon.
 
There are groups and functions within the banks that want MFEs, math PhDs, physics PhDs and so forth. These groups are mainly [Note: I use 'guys' to mean 'guys or girls'] (1) programmers (who write the risk models, electronic trading algorithms, etc.); (2) structured products guys (who put together portfolios of diverse securities tailor-made to a client's risk/return/exposure needs); (3) highly quantitative research guys (who develop proprietary risk-analysis or screening methodologies...though frankly these are a dime a dozen); (4) quantitative risk-management guys (who slice-and-dice the firm's risk exposure, analyze it, stress it, and present the results to management).
 
And even groups in these roles regularly take in candidates without the requisite education and train them up themselves.
 
That said, the vast majority of roles do not require an advanced degree. A typical research analyst uses a pretty basic balance-sheet Excel model, screens for leveraged buy-out candidates with simple rules-of-thumb, and so forth. A typical strategy research analyst uses straightforward regression at most. Real front-office 'revenue generators' (traders, salespeople, investment bankers, etc.) do not need any special training. The banks care primarily about experience...and I can say from personal experience that that's the most important predictor of success in the financial industry. Much of the knowledge required and used here is highly specialized - and the degree of pressure is high. I don't think you'll be able to prepare for it without having to go through the crucible of experience.
 
However, a master's or PhD certainly doesn't hurt. One of the most successful junior salesmen on my desk has an Econometrics MS: a degree he emphasizes is totally worthless. Incidentally, his comments about his job may be relevant: 'How much do I like what I do at work? 3 out of 10. How well-compensated do I think I am for the work I do? 9 out of 10.'

"For example, if a student is working part-time to pay tuition or supporting a family, the extra time required to study for and do well in the Physics GRE can be a barrier."
How is this any different from the general GRE, or doing well in (unrelated) classes, or finding time for research?

I think he was talking about OP. Just a guess

Is this a joke?
If not, you should be aware that this post comes across as extremely arrogant ("excellent research experience (could not be better)", "I have no doubt I will be accepted", etc.), which is not going to play well in a personal statement or at in-person interviews.
As far as target schools go, you need to revise your expectations - a lot. A 3.5 GPA (especially driven by low math grades) puts you pretty far behind the typical admit at most, if not all, of the schools on your list. You need something exceptional to overcome that deficit, and frankly I don't see anything in your record (beyond your claim that people will be blinded by your genius if they meet you in person) that fits the bill. Not to be overly blunt, but Stanford, Wharton, Harvard, Hopkins, and UW are total pipe dreams. UNC and Michigan are pretty big reaches. You might have a better shot at UCLA and Emory, but I wouldn't bet on you being admitted there either.

It would seem like you would have to offer a substantially longer and more sustained response to each of these questions to score above a pretty low grade (around a 2 or so). Especially in the first "evaluate an issue" essay you seem to have a nuanced answer that could very easily sustain a lengthier, fuller, and ultimately better response. It may make sense for you to work on producing such an essay given the time constraints present in the GRE,