Final answer:
The Puritans wanted to establish a 'city set on a hill' in New England to create a model of reformed Protestantism.
Step-by-step explanation:
The people group that wanted to establish a 'city set on a hill' were the Puritans who migrated to New England in the 1630s. They established colonies such as the Massachusetts Bay Colony, the New Haven Colony, the Connecticut Colony, and Rhode Island. The leader of the Massachusetts Bay Colony, John Winthrop, referred to their settlement as a 'city upon a hill' and expressed the goal of creating a model of reformed Protestantism.