It depends on what you are testing with the t-statistic. If you are testing for difference of the sample mean xbar from the hypothesized population mean miu, t = (xbar-miu) /s. e. where s. e. is the standard error. Then t is negative if xbar1 is less than miu. If you are comparing two population means then under the null hypothesis of equality of means t=(xbar1-xbar2)/s. e. (xbar1-xbar2). Then t is less than 0 if xbar1 is less than xbar2.