Taking up the typical test problem of statistical hypotheses, the paper studies fuzzy statistical hypotheses, their test method and its significance. Concretely, the null hypothesis H/sub 0/ that the population mean /spl mu/ is roughly /spl mu//sub 0/(/spl mu/=/spl mu/~/sub 0/) is tested by use of sample data x/sub i/(i=1,...,n) which is independently obtained from normal population, under the alternative one H/sub 1/ that is not roughly /spl mu//sub 0/(/spl mu//spl ne//spl mu/~/sub 0/). Their fuzzy hypotheses bring the possible rejection region and the necessary one corresponding to the conventional method. New aspects of this study are as follows: (1) this method arrives at a soft decision by referring to the grade of the possibility or the necessity that the sample value experimentally obtained belong to the above possible rejection region or the necessary one. On the other hand, the conventional one gives the strict and mechanical decision whether the hypothesis is acceptable or not. (2) The conventional method has the defect that the power of the test heavily decreases at /spl mu/=/spl mu//sub 1/ close to /spl mu//sub 0/ The proposed one can improve the defect thanks to the fuzzy hypotheses.