Explanation:

- The original direct speech statement is: "My cousin said, “My room-mate snored throughout the night.”

- Option 1: My cousin said that her room-mate had snored throughout the night.

- This is correct. The past simple tense in direct speech becomes past perfect in indirect speech.

- Option 2: My cousin told me that her room-mate snored throughout the night.

- Incorrect because it does not change the tense appropriately from direct to indirect speech.

- Option 3: My cousin complained to me that her room-mate had been snored throughout the night.

- Incorrect because "had been snored" is grammatically incorrect.

- Option 4: My cousin said that her room-mate was being snored throughout the night.

- Incorrect because "was being snored" is also grammatically incorrect.