Final answer:
The statement is false; the Puritan influence in New England was well-established by the 1670s due to earlier migrations in the 1620s and 1630s and shaped the region's society, economy, and politics.
Step-by-step explanation:
The statement that Puritan influence in New England had begun to increase by the 1670s even though merchants and other business people increased in wealth is false. By the 1670s, the Puritan influence was already established in New England, having started much earlier with the migration of Puritans in the 1620s and 1630s.
The New England colonies, particularly Massachusetts Bay, Plymouth, New Haven, and Connecticut, were founded between 1620 and 1642 and were profoundly influenced by Puritanism in their social mores, economics, and politics.
Puritans settled in New England with a religious orientation from the start. Their religious beliefs played a significant role in establishing a community focused on church and education. Industry was also important as idleness was seen as the work of the devil.
Puritan settlers hoped a strong economy would evidence God's favor and attract new settlers. Although the merchants and businesspeople accumulated wealth, this did not directly correlate with an increase in Puritan influence, as the socioeconomic structure and Puritan work ethic were already firmly integrated within New England society.