The economic activity that would be common in colonial New England among the options provided is "Shipbuilding and sail repair."
Colonial New England was known for its strong maritime economy, which included shipbuilding as a significant industry due to the abundant forests and proximity to the ocean. While the other activities listed, such as growing cash crops, promotion of the Puritan faith, and signing of the Mayflower Compact, were relevant to the culture and governance of the region, they are not classified as economic activities in the same way shipbuilding and sail repair are.