The shortest confidence interval for the standard deviation and its test in the normal distribution

In this article, based on a random sample from a normal distribution with unknown parameters, we obtain the shortest confidence interval for the standard deviation parameter using the sample standard deviation. We show that this confidence interval cannot be obtained by taking the square root of the endpoints of the shortest confidence interval for the variance given by Tate and Klett. A table is provided to calculate the confidence interval for several sample sizes and three common confidence coefficients. Also, the power performance of the tests made based on the mentioned confidence intervals is considered.