Frank uses improper body position to lift a heavy box and strains the muscles in his lumbar region. which muscles are most likely to be involved in this injury?

Lumbar region refers to the lower back or lower spine.

important muscles of the lumbar spines are:
1) multifidus - stabilizes and rotates the lumbar spine
2) longissimus 
3) spinalis

lower back pain are caused by improper posture, compression fracture, muscle injuries, fractured vertebrae, spinal stenosis, osteoarthritis, herniated disc.