Final answer:
The arrector pili muscles are responsible for causing 'goose bumps' when they contract by pulling on the hair follicles.
Step-by-step explanation:
The muscles attached to the hair follicles that can cause 'goose bumps' when they contract are called the arrector pili muscles. These muscles are found in mammals, including humans, and are responsible for raising the hair when we feel cold or afraid. The contraction of these muscles pulls on the hair follicles, causing the hair to stand up straight and creating the little bumps on the skin known as goosebumps.