No. Generally speaking, employees are entitled to the protections of all employment laws that apply to them, whether federal, state, or local. If more than one law covers a situation, the employer must follow the law that provides the most benefit or protection to the employee. In your situation, this means that your employer must pay the highest applicable minimum wage, not the lowest. If your state requires employers to pay a minimum wage that's more than the federal minimum wage (currently $7.25), you are entitled to the higher state amount. For more information, see Nolo's article Your Right to the Minimum Wage.