@novafan1225, The EFC (estimated family contribution) and your family budget is different.
EFC is the number you get if you complete the FAFSA. If the EFC is low ($5k or less) a student may qualify for a federal Pell grant (up to about $5k/year). The Pell grant is phased out at an EFC of about $5k, so a student whose EFC is $0 will get the whole Pell grant, but a student with an EFC around $5k probably won’t qualify for more than a few hundred dollars, if that.
If a student’s EFC (as calculated by the federal government) is low enough she’d qualify for a Pell grant AND, as a NYS resident, for a NYS TAP (tuition assistance) grant. That’s important because together they can add up to about $10k/year for low income student. (In NYS that can be stretched far enough to pay to commute to a local SUNY).