if t-statistic > Crictical value…we can reject the null hypothesis if t-statistic < Critcical value…we fail to reject the null is this correct??

I think it would be more correct to say that you reject the null hypothesis if the t-statistic has a greater absolute value than the absolute value of the critical value. For example, if you compute a t-statistic of -10 and have a critical value of -2, the t-statistic is less than the critical value. Nevertheless, the null should be rejected.

You are correct!!