Final answer:
The Nobility was extremely important in Shang society due to their belief in ancestral spirits.
Step-by-step explanation:
The family that was extremely important in Shang society due to their belief in ancestral spirits was the nobility.
The Shang royal family considered their ancestors to be powerful entities who could help or harm their descendants. The nobility, which comprised clans closely linked to the king, worshipped their own ancestors but acknowledged the special power held by the Shang royal ancestors. The king relied on the nobility for support and often consulted with them through the use of oracle bone inscriptions.
This belief in ancestral spirits and the role of the nobility in the royal court highlight the theocratic dimension of Shang society, with the king as the intermediary between the people and the spirit world.