Final answer:
The accessory nerve is tested during shoulder muscle strength tests, specifically assessing the function of the sternocleidomastoid and trapezius muscles, which it innervates.
Step-by-step explanation:
The cranial nerve being tested during the muscle strength test for shoulders is the accessory nerve. This nerve innervates the sternocleidomastoid and trapezius muscles, both of which are involved in movements of the neck and shoulders such as head flexion, extension, and shoulder elevation. Motor function of these muscles is assessed by asking the patient to perform actions like flexing and extending the neck or shrugging the shoulders against resistance. Observing lateral differences in strength or a reduction in overall muscle strength can indicate deficits in the accessory nerve or other components of the motor system.