Confidence that a statement is false

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As a software developer, I have made a program that uploads files one by one to a blob storage in the cloud. After the upload is supposedly complete, a different method will try to verify that the upload was successful, and based on the outcome of this verification I get log statements saying whether the upload went ok or not.

Recently, I saw about 2400 log statements saying that the upload had failed. Out of these 2400 error messages, I took 20 random ones and manually checked, but found that the files had been uploaded. So out of 2400 error messages, I found that 20 out of a sample of 20 that those error messages were wrong.

Rerunning the verification process is unfortunately not easily done since it will disturb the data, i.e. data being uploaded agin. Therefore I wanted to see if I could use math to conclude whether all error messages can be ignored, but my knowledge on statistic is too rusty. So the question is basically, with what confidence level can I state that all error messages can be ignored?