In this paper, 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 Colette.We also provide a table for calculating this confidence interval in terms of several sample sizes and common confidence coefficients.Considering the relationship of the confidence interval to the hypothesis testing problem, the power performance of several tests constructed based on the mentioned confidence intervals is compared.
Esmailzadeh, N. & Fazli, K. (2022). The shortest confidence interval for the standard deviation and its test in the normal distribution. Andishe_ye Amari, 27(1), 41-49.
MLA
Esmailzadeh, N., & Fazli, K. "The shortest confidence interval for the standard deviation and its test in the normal distribution", Andishe_ye Amari, 27, 1, 2022, 41-49.
HARVARD
Esmailzadeh N., Fazli K. (2022). 'The shortest confidence interval for the standard deviation and its test in the normal distribution', Andishe_ye Amari, 27(1), pp. 41-49.
CHICAGO
N. Esmailzadeh & K. Fazli, "The shortest confidence interval for the standard deviation and its test in the normal distribution," Andishe_ye Amari, 27 1 (2022): 41-49,
VANCOUVER
Esmailzadeh N., Fazli K. The shortest confidence interval for the standard deviation and its test in the normal distribution. Andishe_ye Amari. 2022;27(1):41-49 (In Persian).
