When calculating the confidence interval for the population mean and the variance is unknown, I take it that you have to use the t-distribution.
However, do you use the one-tailed or two-tailed test values for $\alpha/2$?
It depends on your alternative hypothesis about the mean. If your alternative hypothesis is: true mean is not equal to 0, that means true mean can be both greater than 0 or less than 0. Thus it becomes a two tail test. If you are using R, you may find this link useful: http://www.r-tutor.com/elementary-statistics/interval-estimation/interval-estimate-population-mean-unknown-variance
A (1 - a) confidence lower bound for the distribution mean is:
A (1 - a) confidence upper bound for the distribution mean is: