Question

If I say the difference between two means can be explained by sampling error alone would I reject or fail to reject the null hypothesis? Why?

Answer 1

when we say that the difference between two means can be explained by the sampling error alone, then this means that the sampling error is large enough to fail us to reject the null hypothesis.

When the sampling error alone explains the difference between two means then this tells us that the observed p value must be greater than the significance level for the hypothesis test. This means we fail to reject the null hypothesis

When the sampling error is small, we reject the null hypothesis and this is possible only when the p value corresponding to the test statistic is significant enough.