The word "convey" generally means to communicate or make known. Let's analyze the sentences based on proper usage:
- Correct: The politician has decided not to convey the result of the election.
- Incorrect: Their assignment was to convey the local population on an issue. (It should be "convey to the local population" or "inform the local population.")
- Incorrect: It was difficult to convey, how much we appreciated their help. (The comma is unnecessary. It should be "to convey how much we appreciated their help.")
- Correct: She called to convey that the meeting time had been changed.
- Incorrect: Their policy is to convey payment until repairs are satisfactorily completed. (It should be "to withhold payment" instead of "convey payment.")
So, the correct sentences are 1 and 4. Sentences 2, 3, and 5 contain issues with the use of "convey."