If the population follows a normal distribution, the confidence interval is _____ and can be applied to any sample size. If not, the confidence interval will be _____.

The correct response indicates that when the population follows a normal distribution, the confidence interval can be considered exact, meaning it accurately represents the range within which we expect the population parameter to fall with a certain level of confidence, regardless of the sample size. This is because the properties of the normal distribution ensure that the sample means will also be normally distributed if the population is normal, allowing statisticians to apply the standard formulas for calculating confidence intervals accurately.

In contrast, if the population does not follow a normal distribution, the confidence interval then becomes approximate. In this situation, the assumptions underlying the calculation of confidence intervals may not hold true, especially with smaller sample sizes. Therefore, alternative methods or larger sample sizes may be needed to achieve reliable estimates.

Understanding this distinction is crucial for accurately interpreting confidence intervals and making informed decisions based on statistical analysis. It highlights the importance of assessing the distribution of the data before applying statistical techniques that depend on these assumptions.