Why would you say 'An Hypothesis', not 'A Hypothesis'?
You would only say An hypothesis if you didn't pronounce the "h". And since the "h" is there to be pronounced, not dropped, you should properly say "a hypothesis."
For some, however, the locally preferred pronunciation of hypothesis is 'eye-pothesis" - so it would be an eye-pothesis for them.
You only use an before vowel sounds, regardless of the letter.
A once in a lifetime offer. ["a wunce"]
An hour has 60 minutes. ["an our"]
You'll see references to
An history lesson
but when you do, you must imagine that the speaker is really saying
An 'istory lesson.