# Two Sample t-test gives p-value of zero?

I have two data sets, both are normally distributed (p<0.05). When I run a two sample t-test to assess if there is a significant difference between the means, I get a p-value of exactly zero?

What does this mean? I have never encountered it before. Below is the output from Minitab for the test.

Thank you all for your time. Regards, Tom

Two-sample T for 50_0.22 vs 50_0.12

N    Mean  StDev  SE Mean
50_0.22  4709  1.48   1.48    0.022

50_0.12  4709  1.23   1.00    0.015

Difference = μ (50_0.22) - μ (50_0.12)
Estimate for difference:  0.2477
95% CI for difference:  (0.1967, 0.2986)
T-Test of difference = 0 (vs ≠): T-Value = 9.53  P-Value = 0.000  DF = 8286

• Your first sentence makes no sense. The p-value you mentioned is presumably for a test of normality, but if p<0.05 that would imply a rejection at the 5% level (or if you're not testing at that level, why mention 0.05 at all?). On the other hand, if you meant p>0.05, that does NOT imply that the samples were actually drawn from normal distributions; you should not use that as a basis to claim that they are. On the notion of applying formal tests of distributional assumptions in this manner, see Harvey's answer here Apr 7, 2018 at 10:06