If a 95% confidence interval for a mean difference includes zero, what does this imply?

If a 95% confidence interval for a mean difference includes zero, what does this imply?

• A. The p-value is less than 0.05
• B. The result is statistically significant
• C. The result is not statistically significant at the 0.05 level
• D. The sample size is large

Answer: (C)

The key idea is that a 95% confidence interval for a mean difference represents a range of values that are plausible for the true difference given the data. If zero lies inside that interval, it means a difference of zero is among the plausible values, so we don’t have enough evidence to conclude a real difference at the standard 5% significance level. In hypothesis-testing terms, the p-value for testing no difference would be at least 0.05, so we fail to reject the null. If the interval had excluded zero, that would indicate a statistically significant difference at alpha = 0.05 (p < 0.05). The inclusion of zero doesn’t tell us about sample size by itself; the interval’s width reflects both variability and sample size, and it’s possible to have a large sample where the interval still includes zero if the true difference is small or the data are noisy.

The key idea is that a 95% confidence interval for a mean difference represents a range of values that are plausible for the true difference given the data. If zero lies inside that interval, it means a difference of zero is among the plausible values, so we don’t have enough evidence to conclude a real difference at the standard 5% significance level. In hypothesis-testing terms, the p-value for testing no difference would be at least 0.05, so we fail to reject the null.

If the interval had excluded zero, that would indicate a statistically significant difference at alpha = 0.05 (p < 0.05). The inclusion of zero doesn’t tell us about sample size by itself; the interval’s width reflects both variability and sample size, and it’s possible to have a large sample where the interval still includes zero if the true difference is small or the data are noisy.