Hypothesis tests are a statistical decision-making tool for testing if a hypothesized parameter value is supported by the sample data or not. Vagueness and impreciseness in the sample data require fuzzy techniques to be employed in the analysis. These techniques can be based on intuitionistic fuzzy sets, hesitant fuzzy sets, type-2 fuzzy sets, neutrosophic sets, or spherical fuzzy sets. In this paper, Z-fuzzy numbers are used to capture the vagueness in the sample data and develop Z-fuzzy hypothesis testing. A Z-fuzzy number is represented by a restriction function that is usually a triangular or trapezoidal fuzzy number and a reliability function representing the confidence level to the restriction function. Illustrative examples for left and right sided hypothesis testing and sensitivity analyses are presented.