I have been offered a Ph.D. position in the USA where the offer says 'the admission comes with an 11 month per year teaching assistantship that carries a $2,000/month stipend, health insurance, and a scholarship to cover your tuition. My question is why do they mention 11 months? Does that mean that I will not get payed for the 12th month? I am an international student so I am very confused about the offer. Should I ask the program coordinator regarding this?
It is likely that it means that duties will extend for up to 11 months. But most places like to spread the payouts over 12 months as it eases the bookkeeping process somewhat.
But yes, you can ask.
Likewise health insurance is most likely to extend over 12 months if the award continues.
In the US, however, every university sets its own policies to some extent, so you need to ask.
It may be that 11 months (rather than 9) is to satisfy the visa people. I don't know the regulations for that, however.