Your decision will depends on the probability returned by the t-value that you got. and the alpha level that you choose.

Suppose that you got a t-value equals to 2.04 with 30 df which is the same value founded in the t-table. This value gives u a p-value off 0.05, so suppose that you set alpha to be equals 5%. In this case you will reject the null hypothesis in favor of the alternative one.

Basically you will use the t-value to found the probability and use the probability value to accept or reject a null hypothesis according to alpha.

1) Null Hypothesis Significance Testing (NHST) is flawed in the first place and should not (solely) be used to make decisions. The t-value and hence the p-value is directly dependent on the sample size. This means that you can find a (statistical) significant result for a negligible difference, when you have a large sample size or a non-significant result for a large effect, when you have a small sample size. So, to use NHST appropriately, you have to define an effect size (ES) for the difference (or the parameter of interest, e.g. regression weight), which is of practical significance (in contrast to statistical significance). With this ES you should conduct an a priori power analysis to determine the appropriate sample size.

2) Assuming that you did the afore mentioned steps, then you have to keep in mind that this ominous 5% value is not a natural law, but a guidance to separate signal and noise (I know that some reviewers seem to have a different view on this topic...). It is much more important to be sure that your model is correctly specified, that you have no outliers, an appropriate sample and that the assumptions are met, so that you can be pretty sure that the parameter estimates are correct. Then you can decide if this fits with your hypotheses and if the ES are large enough to support them.

Reject H0.

But actually, it does not matter.

If you think that rejecting H0 when tobs = tcrit, then choose a more stringent tcrit.

Actually the value of a test statistics is also depends on the sample size. You can also use different value of alpha. However, in that case you may reject the null hypothesis.

There is no consensus on this, but I think the decision rule generally used is this:

If the p-value ≤ α ----> Reject H0 at level α

If the p-value> α ---> Do not reject H0 at level α.

In theory, with continuous statistics, such as T, F, Chi-square, normal and many others, this should not matter since, in these distributions, the probability of the critical point is zero and its exclusion or inclusion in the rejection region of H0 does not change its probability. In practice, it is customary to include the critical point in the H0 rejection region.

When the test statistics are discrete, such as Binomial, Poisson, hypergeometric, Wilcoxon, Kruskal-Wallis and many others, it is necessary to be careful so that the probability of the H0 rejection region is less than or equal to alpha.

It is easier to use the p-value, since the decision rule is defined uniquely: if the p-value is less than or equal to alpha, H0 is rejected.

At what point do you accept or reject a null hypothesis