Can I be admitted into a PhD program with non-thesis MS degree? If I do a non-thesis MS program in statistics, will I be eligible for an admission in to a PhD program in Statistics later in my life? The MS program I am looking into is a non-thesis program but I still have to complete a research project requirement (which involves oral presentation as well as some form of a written report) towards the end of the program...I am still not sure if it can lead to a PhD program though.

Thanks!
It depends on the university. Some Ph.D. programs have extra requirements for students who did not complete a thesis (or they will not accept these students). Others are fine with a 'capstone/directed project' which has elements of a thesis. Others may simply ask that students who did not complete a thesis take the GRE for admission into the Ph.D. program while not requiring this for students who did complete a thesis (I attend an R1 university in the US and this is the case here).

So the answer is yes, but it depends on the university.