# T-test and Critical T-values

In order to reject or accept a null hypothesis, we have to check whether the t-test value lie between the critical range or not, but we can’t base our decision on the critical t-value, right?

Clarifying my point through an example:

Say that I want to see whether the null hypothesis will be rejected at a 5% level of signigicant for a two tailed test.

coefficient=0.232

slope=0.098

my t-value is =0.232/0.098=2.367

do I need to calculate the critical t-test which is 0.232+(.098*2.145) or can I compare the 2.367 with the 2.145 directly?

As far as I can tell what you call “critical t-test” is the upper value of your confidence interval. What you need to compare is your t-value (2.367) and the critical value (2.145).

Please also note that your t-value tests the null hypothesis that the coefficient is zero (not sure if that is what you intended to test).

You are right in comparing t critical with t statistic in order to determine significance , but your formula is calculating the confidence interval not the t value

I think I was confused between two points;

1. Acceptance and rejection of the null (this is test through comparing T-test to the critical T; which is determined from the table directly.
2. In case I rejected the null, I would like to know the range out of which I will be rejecting the null which is the level of confidence intervale. In that case the absolute figure of the T-test has to be greater than the absolute value of the equation "0.232+(.098*2.145)" indicated above.

My last question is there a difference between the critical t-value and p-value?

In general, yes. A p-value corresponds to a calculated test statistic (t, z, f, chi-squared) and depends on the data while a critical value does not depend on the data and is based on the preselected alpha or confidence level.