/sci/ - Science & Math

>>7284872
I asked this elsewhere, but because my question is so hard to word, I'm struggling to get an answer.

Pic related, Given that this is a two-tailed test, why does it matter if you use => or =<? I fully understand that as the binomial distribution is not symmetrical and that P(X<=7) is not equal to 1-P(X>=7), the two will give different answers.

I also understand that as 7 is not in the rejection region, the conclusion given by >=7 is clearly correct.

So, I suppose the best way I can word this question is as follows "The question gives us a value of 7 to work with ("Seven of the 12 people said that they preferred blue"), and our hypotheses are:
H0: P=1/3
H1: P is not equal to 1/3.
So how do we know that the right thing to do is consider P(>=7), rather than anything to do with P(<=7)? "

Basically, I'm baffled as to how we go from "the data give us the number 7" to "use >=7", (but I fully understand that >=7 must be correct)