For a directional hypothesis, a one-tailed is most appropriate. If your statistics program have given you a two-tailed test in this situation (which they normally do by default), you could just divide the p-value you have gotten by 2 to get the one-sided p-value :-)

A 2-tailed test is more "conservative," or more cautious, in the sense of making it less likely the researcher will erroneously reject a null hypothesis that is actually true. In other words, with a 2-tailed test the effects or differences found in the sample have to be stronger in support of your alternative hypothesis, in order to reach "statistically significance," than they would need to be with a 1-tailed test. You could use that extra fact as justification, if you decide to use the 2-tailed results.

Or, assuming a 1-tailed test is legitimate (i.e., if you have an a-priori directional alternative hypothesis), you can easily convert the p-value from a 2-tailed test into the corresponding p-value for a 1-tailed test. The latter is simply one-half of the former, as almost any introductory stats book will certify. So a 2-tailed p of .098 is "non-significant" at the conventional .05 level, whereas the exact same sample results give a "significant" p of .049 (= .098/2) in a 1-tailed test.

Using a 2-tailed p of .098, you would fail to reject the null hypothesis at the .05 level. If that null hypothesis is actually true (of course, unknown to you), you have avoided error in your conclusion by not rejecting it. However, if the null isn't true, you have made what is often called a Type 2 error by failing to reject a false null.

Conversely, using the 1-tailed p of .049, you would reject the null at the .05 level. If the null hypothesis is actually false (again, unknown to you), you have avoided error. If it is not false, you have made a Type 1 error by rejecting a true null.

Thank you, Christer Thrane and Burke D. Grandjean for your detailed responses.