Final answer:
The involuntary muscle in the base of the hair follicle is the arrector pili, which is responsible for making hair stand up in response to stimuli such as cold or fear.
Step-by-step explanation:
The small, involuntary muscle fiber in the base of the hair follicle is the arrector pili. This smooth muscle is activated in response to external stimuli, such as cold or fear, which triggers the muscle to contract, pulling on the hair follicles and causing the hair to "stand up". The arrector pili muscle is under involuntary control, similar to other smooth muscles that move internal organs; the cells contain a single nucleus, are spindle-shaped, and do not appear striated. Surrounding the base of the hair follicle is a glassy membrane layer of connective tissue called the hair bulb, which connects the follicle to the dermis. The hair bulb encompasses the hair papilla, a mass of connective tissue, blood capillaries, and nerve endings, as well as basal cells of the hair matrix that differentiate into keratinocytes making up the hair filament.