Intuitionistic fuzzy sets theory, one of the theories used to model uncertainty, is quite successful in modeling real life uncertainties. Hypothesis testing is one of the essential tools in statistics. The methods that are combination of intuitionistic fuzzy set and statistics theory give remarkably good results in cases where the assumptions of classical methods can not be provided. In this study, the theoretical structure of intuitionistic fuzzy hypothesis testing where both data and hypothesis are triangular intuitionistic fuzzy numbers are defined for some population parameters. Also, a new ranking method based on intuitionistic fuzzy number is used to give decision in statistical hypothesis. The applicability of the intuitionistic fuzzy hypothesis testing is demonstrated on several data sets. According to results, an alternative method is presented to the researchers who want to prevent loss of information without converting fuzzy numbers to crisp numbers.