Final answer:
If a confidence interval includes zero, the results are not statistically significant, indicating that there is insufficient evidence to reject the null hypothesis at the chosen level of significance.
Step-by-step explanation:
If a confidence interval for a parameter includes the value zero, then typically, the results are not statistically significant. This is because zero usually denotes the null effect for many statistical tests, such as a test for the difference between two means or a test for a correlation coefficient. If the interval contains zero, the data do not show sufficient evidence to reject the null hypothesis at the chosen level of significance.
For example, if the null hypothesis is that there is no difference between the means of two groups, and zero falls within the confidence interval of the difference, we cannot conclude that there is a statistically significant difference between the means. Similarly, if we are testing whether a correlation coefficient is different from zero and the confidence interval includes zero, there is not enough evidence to suggest that there is a significant correlation.
In summary, a confidence interval containing zero suggests that the null hypothesis should not be rejected. This is a crucial concept in hypothesis testing and statistical inference, emphasizing the importance of the significance level and the comparison of the p-value to this threshold.