Would we determine that the sample fell out of the range (reject null) if |p-value| < alpha? If this were a 2-tail test would we look at |p-value| < alpha/2 or just alpha?
The p-value is typically reported for a two-tailed test, just like the t-stats in an ANOVA table. The p-value can take a value between 0 and 1 so there is no need for absolute signs ( I ). Simply interpret the p-value as the level of significance (alpha), do not divide by 2. So if a two-tailed hypothesis test states a level of significance of 5%, coefficients will be significant if p-value < 0.05. If you were to look up the critical t-value in a table, look for the value corresponding with 2.5%. This is because such tables typically report values for a one-tailed test.
Thanks! 