Could someone please explain the logic of the reasoning behind why we reject the Ho if the alpha exceeds the p value
What I understand is that alpha is the probability of making a type 1 error if Ho is true.
P value is the likelihood of getting a value more to the right or left of your test stat if the Ho is true (probability of getting a test stat that favors Ha more)
So if alpha>p value = reject Ho
Then it must mean that if the probability of making an error while Ho is true is larger than the probability of getting a value more the to the right of your test statistic then reject Ho. How does that logic add up? Could someone explain the reason behind the why we reject Ho?
For example if the chance of picking a value that might lead to a improper conclusion while Ho is true exceeds the chance of getting a value more the right than my test statistic I would reject Ho - how does that work?
Thank you