Sample Size: 1000
Observed Proportion: 15.64%
Confidence Level: 95%
Confidence Interval: ±2.25
Range for the true population proportion: 13.39% to 17.89%
Yes. The bigger your sample size, the bigger your ability to see small effects. A test with 1000 elements can only tell apart big effects; a test with 250000 can tell apart much smaller ones. This is the idea of https://en.wikipedia.org/wiki/Statistical_power
Here's an A/B test I recently ran on some notification messages. There were two messages, only difference is the word "new" in there.
A clickthrough 15.64%, B clickthrough 15.95%.About 1000 samples per group. Not sure if noise.