Hypothesis testing is an important tool of statistical decision making. Classical hypothesis testing is based on a known probability distribution with known population parameters. However, since the data generally include vagueness and impreciseness, a fuzzy set approach should be used. In this paper, interval-valued neutrosophic sets (IVNSs) are used for the purpose of making statistical decisions. In the proposed neutrosophic hypothesis testing approach, neutrosophic linguistic data and neutrosophic parameters are used. Left-sided, right-sided and double-sided neutrosophic hypothesis tests are developed, illustrative example and sensitivity analysis are given.