Under U.S. tax law the portion of the scholarship that covers room and board and other incidentals is treated as taxable income. The portion of the scholarship that covers your tuition is not taxable.
The school was required to withhold 30% of the amount of the room and board. If they withheld based on the 30% withholding rate, then your room and board is about $5,300 for the year. Since I assume you do not have a job, your income for the year will be that $5,300. As a single tax payer you would be entitled to a single person's standard deduction which is $6,300. This alone will take your taxable income from $5,300 to $0 (you can't have negative income on the return for purposes of computing your taxes).
The $1,600 the school is talking about is what they sent to the IRS to cover the taxes on your income. However, since you will not have any income you will get a refund of everything sent to the IRS for taxes. The IRS will send back the $1,600 once you file your tax return. If the amount they are looking for comes from taxes payments they sent last year in 2015, all you should have to do is file the tax return for 2015 and the money will be refunded to you so you can pay back the school. I suggest you go to the school scholarship office and review this with them and they can help you get the tax forms you need. The forms are very simple if you use 1040A or 1040EZ. That should resolve the problem and you can stay in the school you are in and do not have to go elsewhere.
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