If a 95% confidence interval for a mean difference excludes zero, what does that indicate about statistical significance at alpha = 0.05?

• A. The difference is statistically significant at the 0.05 level.
• B. The interval is too wide to draw conclusions.
• C. The difference is not significant.
• D. The sample size is insufficient.

Answer: (D)

A 95% confidence interval for a mean difference that excludes zero shows that zero is not a plausible value for the true difference at the 5% significance level. In practical terms, this means you would reject the null hypothesis of no difference at alpha = 0.05, because the data indicate a real difference rather than random variation.

Think of the interval as the range of values compatible with the data for the true difference. If zero lies outside that range, there’s evidence that the true difference is not zero, which aligns with reporting statistical significance (p-value less than 0.05). This does not necessarily imply anything about the need for a larger sample; a result can be significant even with a small or large sample depending on the observed effect and variability.