What is normal pay in U.S. for RAship in STEM field? I am a PhD student in statistics/math in the U.S. I go to a large, state run institution. I am currently hired for the summer as a research assistant for a professor.

On the department website, an RAship is listed as being a 20 hour a week job, paid at $21 per hour. This is what she and I agreed to before my starting researching with her. However, now my professor wants me to work 40 hours a week for $7.34 an hour. (She is actually going to pay me $14.68/hr, since only 20 hours are bookable for legal purposes. Well, and the fact that $7.34 is below minimum wage). I never got the $21 in writing, so that is my error. 

Working 40 hours per week is in essence requisite to retain the job (since the workload she requires to keep the job necessitates such). She is offering me no dissertation credit for my work, only this pittance of a grunt wage. Outside of a weekly hour long meeting via Skype, she does not have any time to mentor or guide me. Her promise is that at some point the research I do for her will become a dissertation topic. But, as of right now, I am just reading papers she is too busy to read and then telling her what they say. 

This professor is not from the U.S. and I believe is somewhat unfamiliar with U.S. practices in fair wages. (For example, she offered me $10/hr to do some other things related to her research for her. I earned more than that as an undergraduate TA for a sophomore level class). I am not asking for $15/hr for flipping burgers, just a fair compensation for the work I am doing for her. She has a large NSF grant that she might end up losing if I do not produce results for her to show them. 

She justifies requiring these hours at this pay because she says that I will end up possibly, maybe, hypothetically, if the moon lands on earth, theoretically finishing a third of my dissertation. 

I am aware that I need to pay my dues so to speak. Naturally, I know that I need to put in a lot of time to a PhD that is not monetarily compensated. Nevertheless, I feel a bit like I am being taken advantage of. Is this pay structure/workload normal for an RAship, or should I take it up further with her?
I only have two US experiences to offer for comparison, one from a public university and another from a private.

The public university pays it's TA/RA's ~$8000 for a 9 month stipend.  The private university pays TA/RA's $19,000 before taxes for a 9 month stipend.  Both have stipulated that the expected workload is 20 hours a week.  While the public university pays significantly less than the private university, the hours for a pure math graduate student rarely exceeded 20 hours per week (new teachers sometimes spend more prepping, but any hourly help session positions were strictly 20 hours).  Paywise, I think the rate you're being offered for a 20 hour work week is not unheard of, especially for a public university.  However, being told you actually have to work 40 hour weeks means you're working for a rate less than the legal limit.  That certainly counts as getting screwed in my book.

Personally, I would say run like hell.  I know that academia has a history of overworking/underpaying graduate students, but I would find an alternative arrangement even if it means finding another school to attend or delaying a year.  Another consideration is that working 40 hours a week makes it difficult to actually do well in your studies and it wouldn't be ridiculous to consider picking up a side job just to make ends meet (meaning you're potentially working 60+ hours a week).  If you enter this arrangement, I suspect you'll be back here asking how to deal with burn out or how to recover from a mental breakdown from stress.  If you seriously want to be successful in your program, you need to find something better.