I am a senior undergrad at Rutgers and have conducted reserach in both the social and cognitive departments
Stat courses: I hear it is comparable to undergrad level statistics. I have taken the advanced statistics course in psychology at this institution for undergrads and it was very easy for me. I hear they are both the essentially the same course in terms of material. However, I imagine the format is slightly different. I know for the Stats 2 (Graduate Level Psychology) course there are a few short papers, a presentation, weekly homework, and exams. It depends on who is teaching the course.
I spent a lot of my time at Rutgers in the social department, so I can't speak exactly for the cognitive deparmtnet, but I don't believe they expect a lot out of you statistics-wise. I am aware of some people who are very solid in their statistics in the cog sci/cog psych department, so if you have a statistics background feel free to sell it but otherwise, I do not believe the expect a lot. Again, this is coming from someone who spent a lot of their time in social. I am sure it also depends on what type of research you are interested in doing.
tldr: They probably don't have a lot of expectations, but there are some really good people in the department so it may depend on who you are interested in working with. I am sure you meet the general requirements for the department, but the more statistics the better.
If you have any further questions, feel free to PM me. Best of luck.