Confidence Interval and Hypothesis Testing: Relationship and Interpretation

If the confidence interval does not contain 0, it means that there is evidence to suggest that the true population parameter is different from 0. In other words, there is a statistically significant difference between the sample mean and the hypothesized population mean of 0.

If we were to conduct a two-sided test at the 5% significance level, we would be testing the null hypothesis that the population mean is equal to 0 against the alternative hypothesis that it is not equal to 0. Since the confidence interval does not contain 0, we would reject the null hypothesis and conclude that there is a statistically significant difference between the sample mean and the hypothesized population mean of 0 at the 5% significance level.