What is a confidence interval?

A confidence interval represents a range of values that are calculated from sample data, which is likely to contain the true value of a population parameter. The key idea is that rather than pinpointing an exact value, a confidence interval provides a spectrum of plausible values, thereby acknowledging the uncertainty that comes with sampling.

For instance, if you were to calculate a confidence interval for the mean height of students at a university based on a sample, the interval might suggest that the true average height falls between 5'6" and 5'10". This reflects the variability and uncertainty inherent in using a sample to make inferences about a broader population.

Moreover, the confidence level, often set at 95% or 99%, informs us about how often we expect the interval to contain the population parameter if we were to take many samples. This aspect of confidence intervals is essential in statistics because it offers a way to quantify the uncertainty surrounding estimates without making definitive claims about the exact values.