Reject 1 tailed test but not reject 2 tailed test I'm going through a statistics course and don't understand this point. 
Since a 2 tailed test has alpha/2, the reject rate moves further down the tails. Would there be a case where you reject a one tailed test (because p< 0.05), but will not reject a 2 tailed test because you have effectively taken the reject rate further down (p < 0.025)  when you divide alpha by 2.
Sorry I'm not getting this point but according to the course if you fail the one tailed test you would also fail the two tailed test. 
 A: I think it might help to think about it visually. Picture a normal distribution bell curve, then imagine shading in one of the tails (right or left) that contains 5% of the total area under the curve. In a one-tailed test, you will reject your null hypothesis if your result falls within the shaded area. Make sense? 
But if you drew the shaded region to the right side of the curve, then you are never going to reject the null hypothesis if your result falls on the left side of the curve--no matter how far to the left it is. 
Now, for the two-tailed version you still need to shade regions that contain 5% of the total area under the curve, but you are splitting it up on both sides of the bell--so each side only gets 2.5% of the total area. Thus, for your result to be significant under a 2-tailed test, it will have to fall a bit farther from the middle of the curve--but, unlike a 1-tailed test, your result can be significant in either direction, left or right. 
So, a hypothetical result could be significant in a 1-tailed test, but not in a 2-tailed test, because it was far enough from the center to fall in the 5% region of the curve, but not far enough out to fall into the 2.5% region. But, it could also go the other way--because the 2-tailed test will allow you to reject the null hypothesis based on results that fall on both ends of the bell curve.
As for weather you should use a 1-tailed or 2-tailed, that should be informed by your hypotheses or question. If you predict that "X will change Y" then use a 2-tailed, if you predict "X will increase Y" use a 1-tail (that's way oversimplified, but the general idea).
