What is a 95% confidence interval?

A 95% confidence interval is fundamentally a statistical range that provides an estimate of where the true population parameter (such as a population mean) is likely to be found. When we create a 95% confidence interval from sample data, we are essentially stating that if we were to take many samples and calculate a confidence interval from each one, approximately 95% of those intervals would contain the true population parameter. This concept is foundational in inferential statistics, emphasizing that the interval is derived from sample statistics and reflects our degree of certainty about the unknown population parameter.

This confidence level—95%—is chosen to express a high level of certainty. It implies that there is a 5% chance that the true parameter lies outside of the computed interval, hence providing a reliable estimate based on the data at hand. Being confident at this level reflects the precision of the sample data used in constructing the interval and conveys how much we can trust our point estimates.

In contrast, the other options do not accurately describe the definition or purpose of a confidence interval. For instance, the first option speaks about sample variability rather than the relationship between sample estimates and population parameters. The third option erroneously defines a confidence interval as merely a measure of sample size, which is unrelated