A confidence interval on standard deviation is a range of values that is likely to contain the true population standard deviation with a certain degree of confidence. It is used to estimate the precision of a sample standard deviation and to determine the variability of a population.
A confidence interval on standard deviation is calculated using the sample standard deviation, sample size, and a critical value from the t-distribution. The formula for calculating the confidence interval is: sample standard deviation ± (critical value * standard error of the sample standard deviation).
The purpose of a confidence interval on standard deviation is to provide a range of values that is likely to contain the true population standard deviation. It is used to estimate the precision of a sample standard deviation and to determine the variability of a population.
The confidence level for a confidence interval on standard deviation is typically chosen to be 95%, 99%, or 99.9%. This represents the degree of confidence that the true population standard deviation falls within the calculated interval. A higher confidence level indicates a narrower interval, while a lower confidence level indicates a wider interval.
The assumptions for calculating a confidence interval on standard deviation are that the data is normally distributed and that the sample is representative of the population. If these assumptions are not met, then the confidence interval may not accurately reflect the true population standard deviation.