When do we use a two-tail hypothesis testing instead of a one tail? I always use a two-tail hypothesis testing unless I am told to use a one tail. Is that a good way of going about solving problems or is there a flaw to that way of doing things?
Also, if they say use a significance level of a = 0.05, does that mean I can choose 0.025 and do a two-tail or a one-tail with 0.05 or does that mean i can only use a one-tail test?
 A: You should learn how to tell the difference and figure out if you need a one-tail or two-tail test without having to be told.  When you first start, your method is good enough, but soon you need to understand why you're doing one or the other.
You start off any test with a null hypothesis and your test is to, essentially, see if it is wrong.  Or, another way to see this, is to see if your alternative hypothesis is right.  So, it depends on what your alternative hypothesis is.
For example, let's say there's a rule on what food manufacturers can call "Low Fat".  And, let's say a company claims that they fit this rule, but maybe someone in the government is not so sure.  In this case, if it turns out that this food has even less fat then they say they have, then they would still be considered low fat, so it wouldn't prove anything wrong.  In this case, we would only care if they had more fat than they said they did.  So, we would use a one-tail test, only rejecting if the fat content is too high.
On the other hand, if it is important to know if the current null hypothesis is wrong in either direction, then we would use a two tail test.  We would reject it if the experimental values came quite a bit higher than the null hypothesis or quite a bit lower.
The significance level is the probability that the null hypothesis is rejected even though it is in fact true.  That means, in calculating the probability, we assume the null hypothesis is true and then calculate the probability that this would be rejected if we run the experiment.  Since we are interested in the probability of rejecting the null hypothesis, it completely depends on if we are doing a one-tail or two-tail test.  And, that's what you need to think about as far as whether you use 0.05 or 0.025 when you are given a significance level of 0.05.  If your test is two-sided, then that means there is should be 0.025 on each side, so you'd use 0.025.  But, if the test is one-sided, your entire probability of 0.05 must be all on one side, so you'd use the 0.05.
A: Whether you do a one or two-tailed test is dependent upon the experiment.  A two-tailed test implies that your error is symmetric around your expected value, which is often the case.  A one-tailed test implies that your error is in one direction.  This is not often the case, but it could be.  So ... to the experiment!
