Example: A Significant, but Potentially Meaningless Difference
Gender N Mean StDev SE Mean
95% CI for mu (1) - mu (2): ( -142, -5)
T-Test mu (1) = mu (2) (vs not =): T = -2.11 P = 0.036
P-value tells us significant difference, but confidence interval tells us that the difference in the averages could be as small as 5 minutes.