Final answer:
True, Sparta never joined the Delian League and was apprehensive of Athens' increasing power, a rivalry that contributed to the outbreak of the Peloponnesian War.
Step-by-step explanation:
The statement is True. Sparta did indeed disapprove of the growing influence and power that Athens was asserting through the Delian League. Sparta, as the head of the Peloponnesian League, which was in direct competition with the Athenian-led Delian League, indeed never joined the Delian League. The friction between the two leagues grew over time, with Sparta becoming increasingly resentful of Athenian power. This growing rivalry and resentment eventually led to the outbreak of the Peloponnesian War in 431 BCE when Athenian attempts to influence the political decisions of Spartan allies escalated tensions to the point of warfare.