> you do have good reason to believe that the choice is harmless.
The issue you will run into here is that 95% confidence means that you will only have a false positive 5% of the time. It does not mean a neutral finding is 95% likely to be neutral. The lever that controls that is statistical power, which is oft-ignored in conversations about A/B testing. Most statisticians use 80% power, which means a full 20% of neutral findings were false negatives.
The issue you will run into here is that 95% confidence means that you will only have a false positive 5% of the time. It does not mean a neutral finding is 95% likely to be neutral. The lever that controls that is statistical power, which is oft-ignored in conversations about A/B testing. Most statisticians use 80% power, which means a full 20% of neutral findings were false negatives.