Hi guys, i am wondering, if significance level is the probability of rejecting the H0 when it is true, why lower significance level needs stronger evidence ? If the probability of being true is lower, I will be more certain when reject, thus, less evidence needed, no?

It’s not the probability of being true that’s lower.

It’s the probability of * rejecting H_{0} when it’s true that’s lower*.

Put another way, it’s the probability of you fouling it up that’s lower.

If you want to make it likely that you’ll foul it up, reject H_{0} on the flimsiest of evidence.

If you want to make it unlikely that you’ll foul it up, reject H_{0} only with overwhelming evidence.

Thank you indeed! You are the magician!

My pleasure.