Education

First of all, lets be clear that "what dollars were used for what" throughout the year does NOT (necessarily)  need to be the same as the way you report it on your tax return.

In other words, you could get a scholarship, pay tuition, pay Room and Board, buy a laptop needed for class, and then rearrange the expenses however is best on your tax return to get an education credit or lower your tax liability.   

Next, I don't think you understand the forms. Box 1 is Only Tuition and fees, no Room and Board. So if box shows 7,110, that is ONLY tuition and fees, NOT Room and Board (even if the room and board was paid to the school) So asking if 4,000 should go to room and board has nothing to do with the 7,100 in box 1 on a 1098-T. Room and board expense does not show on Form 1098-T. 

It can seem a bit complicated, but IRS Pub 970 has some great examples to illustrate the options you might have. 

Ok, so based on your numbers you have 7,110 for tuition and fees expenses paid to the school.

You had 5,303 in scholarships paid in your name to the school.

So right off you have 1,807 expenses to apply towards an education credit.

Now, do you also have Books, Fees, and Supplies to add to your expenses? I do not know that.

Can you apply for the American Opportunity Tax Credit? I do not know that without additional information but if you are eligible, you most likely will want to ty to get it. 

The American Opportunity Tax Credit maxes out with 4000 expenses. 

SO if you already have 1807 in tuition, you max out with 2,193 additional education expenses. 

You could then allocate 2,193 of the scholarship to room and board leaving only 3110 to go toward tuition leaving 4,000 for an education credit (the max) 

This means you will be taxed as income the 2,193, but the credit will more than likely make up for the tax on the income. 

You may need to clarify what numbers are reporting what. Contact the school student aid or school billing records if you are not sure.