One sample t test cases

Question

So I want to know when do we accept the null hypothesis and when we don't in t test.

Case 1: t cal>t tab and p value >0.05,we accept null hypothesis

Case 2: t cal>t tab and p value <0.05 we don't accept null hypothesis.

Case 3: t cal < t tab and p value <0.05,we accept null hypothesis

Case 4: t cal < t tab and p value >0.05,we accept null hypothesis

It this correct?

Answer 1

The rule is

low $p$-value $\Leftrightarrow$ reject the null hypothesis.

So if $p\le 0.05$ (or whatever significance level you set), then you can reject the null hypothesis. Otherwise, you cannot reject it. Currently, you have written $p<0.05$ in all cases, which is not correct.