I am a complete newbie to statistics, and have gotten stuck on a difficult real-world problem.
What I'd like to do is demonstrate confidence that, for a set of < 50 observations of two actions, the time between the two actions was less than an hour. For the first action, I have a timezone-naive timestamp. For the second, I have a timezone-aware timestamp (UTC). The location of the actions is not known. Time between the two actions is known to be less than eight hours.
To visualize the problem, I have removed time zone information from the second action timestamps, subtracted the two, and taken the mod 60 value of the result, to represent the "minute within the hour" of the difference. This results in a histogram that looks like this:
Just from a visual examination, I feel confident that the time between the actions was less than an hour (usually around 5 minutes, as opposed to an hour and five minutes, two hours and five minutes... etc) but I don't know how to express this confidence quantitatively. I'm having a bit of trouble determining what the null hypothesis would be, here. Any insight would be greatly appreciated!