A statistical hypothesis test is an indispensable and powerful tool for making better decisions in various fields. When it comes to tasks involving large populations, it is not always possible to make accurate sample observations. That is, real-time observations may be accurate or imprecise by their nature. If the observed samples are imprecise, the corresponding samples can be manipulated with fuzzy numbers; more generally trapezoidal fuzzy numbers. Moreover, using a new ranking method derived from the lifespan of Euler centroid these fuzzy samples are fuzzy and a relevant statistical procedure was followed to test the hypothesis and obtain better results.