How do you interpret a 95% confidence interval for a mean difference that does not include zero?

• A. The p-value is greater than 0.05.
• B. The result is statistically significant at alpha 0.05; there is evidence of a true difference.
• C. There is no evidence of any difference.
• D. The result is not statistically significant; CI excludes zero.

Answer: (B)

When a 95% confidence interval for a mean difference does not include zero, it means zero difference is unlikely at the 5% significance level. In practical terms, the data suggest there is a true difference between the groups, and the range of plausible differences is entirely on one side of zero, indicating the direction of the effect. Because zero is outside the interval, the p-value for testing no difference is less than 0.05, so we consider the result statistically significant at alpha = 0.05. The endpoints of the interval also give a sense of the magnitude of the difference, though precision depends on sample size and variability. This is why the best interpretation is that the result is statistically significant at 0.05 with evidence of a true difference.