If the calculated t-value is smaller than the critical value of t would we reject the null hypothesis?

Answer 1

It depends what the hypothesis is; especially if the test is left-tailed or right-tailed vs. two-tailed. If it's left-tailed and t < t_crit or right-tailed and t > t_crit, you would reject in both those cases. If it's two tailed, you will reject if | t | > | t_crit | . This is guidline, you really have to apply this to a particular problem and notation.