Hypothesis Test using p values

Question

Can someone clarify this:

My text states: If the computed p-value is less than or equal to alpha, reject the null .... If the computed p-value is greater than alpha, then fail to reject the null ...

But the software accompanying the text states: Is the p-value less than the level of significance? If yes, reject the null hypothesis .... If no, fail to reject the null hypothesis ....

Which is correct? If I go by prior discussions in the text where we use z and z_critical to make a decision, the rule was to reject the null if z > |z-critical|. If z exceeds |z-critical| then the corresponding p-value (for z) must be smaller than the corresponding alpha value (for z-critical) to reject the Null. So the z > |z-critical| rule agrees with what the software says about using p values. So, is the rule stated in the text incorrect? Is the software incorrect? Or, am I wrong in my reasoning? Thanks.

Answer 1

Those statements do agree. The text statement says that if (and only if) the computed $p$-value is less than some level ($\alpha$, which might be say 5%) then reject the null hypothesis. Of course, this rejection happens when the $z$ quantity is greater than some critical $z$ which depends on your selected $\alpha$.

The software statement is that if $p$ is less than the level of significance (which would be that same 5%) then yes, reject the null hypothesis; if not, then fail to reject. This is exactly the same as the text statement.