When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and standard deviation, one can construct confidence intervals for the population standard deviations at a suitable significance level, such as 95%. A confidence interval is an interval of numbers. It provides a range of reasonable values in which we expect the population parameter to fall. There is no guarantee that a given confidence interval does capture the population standard deviation, but there is a predictable probability of success. The critical values in the right and left tails of the distribution curve provide the confidence intervals of the population standard deviation.
This text is adapted from Openstax, Introductory Statistics, Section 8, Confidence Interval
