Final answer:
The tiny, involuntary muscle fiber in the skin inserted in the base of the hair follicle is called the arrector pili.
Step-by-step explanation:
The tiny, involuntary muscle fiber in the skin inserted in the base of the hair follicle is called the arrector pili. When this muscle contracts, it causes the hair to stand up, a phenomenon commonly known as goosebumps. The arrector pili muscle is activated in response to external stimuli that pull on the hair follicles.