Is It a Real Pattern: The Magic of Tuesday at 11

A colleague running the social media says: "Posts I put up at 11 a.m. on Tuesday always do well. I'm going to post all the key posts of this campaign at that time." When you check, of the 40 posts over the last three months, 3 were posted at 11 a.m. on Tuesday, and 2 of those got more likes than average. But those 2 were both posts that mentioned a celebrity.

Design a way to tell whether 'posts at 11 a.m. on Tuesday do well' is a real pattern or coincidence. Your answer must include (1) how the data should look if this pattern is real versus if it's coincidence, (2) what and how much more you'd collect or compare, and (3) what evidence would refute this pattern.