Determine 1 tail or 2 tail test

I get confused as to when to consider a 1 tail or 2 tail test…can someone please clarify?

2-tail: testing whether or not a coefficient equals “X” (typically testing whether or not a coefficient has any statistical signficance, ie if the coefficient is signficantly different from zero).

1-tail: testing whether or not a coefficient is greater than or less than “X”.

If H0: x=0, Ha: x NOT= 0 To reject the null, you can show that x > 0 or x < 0, these are two cases, so it’s 2-tailed test. If H0: x<=0, Ha: x > 0 To reject the null, you try to show that x > 0, that’s a 1-tailed test.

To expand on this, I want to confirm when you are testing for significance on a two tailed test and they state 95% , I assume you would use .025% to find the critical t value since we’re looking at the negative and the positive side of the distribution. And, if we were doing one tailed then it would be .05% since it’s only side of the distribution so all 5% should be located there. Can someone confirm this?

That’s correct swt326. Think about it. If someone says x=5, it might be quite easy to prove them wrong because if you calculate x=4.99, they are wrong! They said x=5, but you found x=4.99. You can reject their claim. However, that’s not fair, so they set for example 2.5% above or below that and challenge you to prove them wrong. With x=4.99, that’s not enough to reject their claim. What if you found x=4.95, what would you do?