If a 95% confidence interval for a mean difference includes zero, what does that imply at alpha = 0.05?

• A. The result is statistically significant at the 0.05 level.
• B. The result is not statistically significant at the 0.05 level.
• C. The effect size is large.
• D. The sample size is insufficient.

Answer: (B)

A 95% confidence interval for a mean difference shows the range of values that are plausible for the true difference given the data. If zero lies inside that interval, you cannot rule out no difference at the conventional 5% level. In hypothesis-testing terms, a two-sided test with alpha = 0.05 would not reach significance because the null value (zero) is compatible with the data, leading to a p-value greater than 0.05. This means there isn’t enough evidence to claim a real difference at that level, even though the interval includes zero. It doesn’t imply a large effect or certain structural issues with the sample size; it just reflects the level of statistical evidence given the data.