What should I check first when a regression table seems to pair a strong t-statistic with an insignificant p-value?

Check the row alignment first. Regression tables often show several coefficients, standard errors, t-statistics, and p-values. A strong t-statistic for one coefficient can sit near a high p-value for another coefficient.

Then check the test direction and tail convention. For a two-tailed coefficient test, a large absolute t-statistic should generally mean a low p-value. If that is not true, the p-value may be from a different row, the question may be using a one-tailed alternative in the opposite direction, or the statistic may not be a t-statistic for that coefficient.

Exam decision rule:

p-value <= alpha: reject H0
p-value > alpha: fail to reject H0