Final answer:
The incorrect statement is b) The Spartans controlled the Delian League for over 50 years. It was Athens that controlled the Delian League and used it to create an empire.
Step-by-step explanation:
The statement that is NOT correct is b) The Spartans controlled the Delian League for over 50 years. The Delian League was indeed formed during the Persian War, which makes statement a) correct. Statement c) is also correct as the Peloponnesian League was formed after the Persian War.
Additionally, statement d) is correct because the Peloponnesian League was disbanded decades after the Peloponnesian War.
It is crucial to note that the Delian League was primarily under the control of Athens, not Sparta. Athens used the Delian League to build its naval power and exert control over other Greek city-states, turning the league from a mutual defense against Persia into an Athenian Empire.