Final answer:
If a confidence interval includes the null hypothesis value, then the results are not considered statistically significant, indicating insufficient evidence to reject the null hypothesis at the given level of significance.
Step-by-step explanation:
If a confidence interval contains the value 1, then the results are not statistically significant. This is because the confidence interval range includes the null hypothesis value (often 1 for ratios or differences, and 0 for differences or correlation coefficients), which suggests that there is not enough evidence to reject the null hypothesis. In other words, the data does not provide sufficient evidence to conclude there is a difference or effect.
A commonly used level of significance is 5 percent (alpha = 0.05). If the p-value is greater than or equal to 0.05, the decision is to not reject the null hypothesis. This aligns with the situation where a confidence interval contains the null hypothesis value and indicates that the results are not significant.
To describe what a confidence interval means in general: A confidence interval provides a range of values which are estimated to contain the true population parameter with a certain level of certainty (for example, 95% or 99%). If the interval includes values that represent 'no effect' or 'no difference', it suggests that there is no statistically significant difference or relationship.