The GPA would not need to be exceptionally high, unless you mean 3.75-3.8.
What @Johnny_L would need to do is a thesis masters in which he demonstrated the ability to do research. That likely means a thesis which has at least one publishable article, and good LoRs from the faculty.
The weakness of the OPs application for a PhD programs that I can see is that they have no research experience, no interactions with faculty, etc.
I knew somebody back when I was a grad student who finished her BSc with a 2.7 GPA, and was accepted to a good PhD program. She had been working as an undergrad in the lab of a really top researcher in the field, and her field work, personal research, and a glowing, personal LoR (and a well written statement of purpose) got her into the program. Her GRE scores were good, but not great.
Mind you, a high GPA would help in admissions, but without that demonstration of research abilities, a GPA of 4.0 for a masters program will not make the OP very competitive for any good PhD program.
Truth is, getting a high GPA in a masters program is not all that difficult. A masters student is taking courses in their field of choice, which they are interested in, and in which they have decent level abilities. I have had very few thesis masters students who have gotten Bs and none who have gotten Cs.
The old saying for graduate students is that the grades go like this:
A - Average
B - Below average
C - Confused. Too Confused to have dropped the course.
Unlike PhD students, masters students are not ensured financial support. So unless you are independently wealthy, you will not be able to afford a masters in any private university. Your profile, as you present it, indicates that receiving merit support is unlikely. Masters programs in these universities are extremely competitive, and it is unlikely that you will be accepted, unless all of your grades in your major courses are As.
You need to find a solid masters program which will accept you, and work hard, and demonstrate top abilities in research in order to have a chance for admissions to one of these programs.
Here is an important question - do you know what a PhD student in statistic does? PhD research is statistics is radically different than taking courses and learning how to use statistics, and how to understand statistics.
Before you commit to trying to go off and do a PhD in statistics, you first need to figure out whether this is something that you want to do and are willing to do, and whether it is something that you are able to do.
Finally, forget about “dream schools”. You don’t know what a school’s graduate program looks like, what the work is like, what the faculty and students are like, or what it is like to be a graduate student at any university. You also do not know whether anybody is working on a topic that interests you enough that you would want to spend 5-7 years working a small part of that topic. As far as you know, being a graduate student at Cornell could be a nightmare for you.