Final answer:
Denate nuclei in the deep cerebellar area are responsible for the planning, initiation, and control of volitional movement, which is the correct statement regarding their function.
Step-by-step explanation:
The correct statement about deep cerebellar nuclei is: D. Denate nuclei are responsible for planning, initiation, and control of volitional movement. The denate nuclei project to the premotor and motor cortices and play a critical role in the planning and initiation of voluntary movements. They are not responsible for directly sending information to lower motor neurons. The interposed nuclei, which include the emboliform and globose nuclei, have a role in controlling and coordinating movements, but do not send information directly to the premotor cortex; instead, they influence movements more indirectly. The fastigial nuclei are implicated in the modulation of muscle tone and balance, especially tied to antigravity muscle groups, and are not primarily focused on distal muscle group reflexes.