Even my own son asks me this question.
Question: As a full-time student, am I exempt from federal taxes?
Answer: There is no exemption from tax for full-time students. Every U.S. citizen or resident must file a U.S. income tax return if certain income levels are reached. Factors that determine whether you have an income tax filing requirement include:
The amount of your income (earned and unearned),
Whether you are able to be claimed as a dependent,
Your filing status, and
Your age.
If your income is below the filing requirement for your age, filing status, and dependency status, you will not owe income tax on the income and will not have to file a tax return. You may choose to file if you have income tax withholding that you would like refunded to you. For more information on filing requirements refer to Publication 501, Exemption, Standard Deduction and Filing Information.
You may have given your employer a Form W-4,  Employee’s Withholding Allowance Certificate, claiming exemption from withholding. To claim exemption from withholding, you generally would have to have had no tax liability the previous year and expect none in the current year.  An exemption certificate is good for the calendar year.