When a student raises her hand so that she can answer a teacher's question, the branch of the peripheral nervous system was responsible for her hand going up.

motor (efferent)

Explanation:

The somatic nervous system is the component of the motor division of the peripheral nervous system. The motor division of the peripheral nervous system carries the motor information from the central nervous system to the muscles and/or glands. The motor branch includes the somatic and autonomic nervous system. The somatic nervous system of the motor branch delivers the motor information from the CNS to skeletal muscles resulting in the generation of voluntary responses such as raising hand in a class.  

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