Abstract
The Sign test is a famous nonparametric test from classical statistics used to assess the one or two sample averages. The test is practical when the sample size is small, or the distributional assumption under a parametric test does not satisfy. One of the limitations of the Sign test is the exact form of the data, and the existing methodology of the test does not cover the interval-valued data. The interval-valued data often comes from the fuzzy logic where the experiment's information is not sure and possesses some kind of vagueness, uncertainty or indeterminacy. This research proposed a modified version of the Sign test by considering the indeterminate state and the exact form of the data-the newly proposed sign test methodology is designed for both one-sample and two-sample hypothesis testing problems. The performance of the proposed modified versions of the Sign test is evaluated through two real-life data examples comprised of covid-19 reproduction rate and covid-positive daily occupancy in ICU in Pakistan. The findings of the study suggested that our proposed methodologies are suitable in nonparametric decision-making problems with an interval-valued data. Therefore, applying the new neutrosophic sign test is explicitly recommended in biomedical sciences, engineering, and other statistical fields under an indeterminate environment.