A problem asked me to explain why a $99\%$ confidence interval of the difference of two sample means did not offer substantial evidence of a difference in the two populations. The interval was something like $(1,11)$ and clearly didn't include $0$.
I was under the impression that if $0$ is an unlikely difference value, then there is evidence that the two population means are different.
What am I not understanding? Did I possibly overlook some essential info?