Historically, this issue and question of whether and how people's religion is related to their position in the social stratification system has been a subject related to sociologists in different time cycles of sociology since the beginning of its development. The review of the theoretical literature in this field of study showed that the scientific answers to the mentioned question can be generally found under the two theories of deprivation and relative power in the sociology of religion, which make opposite predictions about the distribution of levels of religious commitment in the social stratification system. This research article was compiled for the purpose of experimentally Testing the competing hypotheses arising from the two theories of deprivation and relative power in explaining the relationship between class and religious commitment. In this regard, these competing hypotheses were confronted with the data obtained from a national survey of 82,500 Muslim Iranians in order to evaluate their conformity and correspondence with empirical evidence. In sum, the findings of this research showed that the relationship between class and religious commitment among Iranian people was mainly in a direction compatible with the theory of deprivation and for the main claim of the mentioned theory, it has a confirmation meaning. Secondly, because the main argument of the theory of relative power involves a hypothesis that is contradictory to the theory of deprivation, the empirical verification of the theory of deprivation logically requires the rejection of its opposite theory, that is, the theory of relative power.

Fuzzy set theory models situations in which the uncertainty is due to the non-precise (fuzzy) environment. One such case is Testing the hypotheses problem where hypotheses are fuzzy rather than crisp and the data are crisp. Pais and Benton (1997) [1] present a suitable amount of cadmium absorption which is more appropriate for modeling by a fuzzy subset. In this paper, on real-world agricultural data generated by Ivani (2007) [2], the suitableness of the mean absorption cadmium in the plant from the polluted soil is tested at the given significance level. Due to uncertainty in the suitable amount of cadmium absorption, in order to test this amount, we use fuzzy hypotheses Testing instead of classical hypotheses Testing. The fuzzy p-value approach is used for this test to conclude whether or not the mean absorption of cadmium coincides with the proposed amounts by Pais and Benton [1]. As expected, in fuzzy hypotheses Testing, the degree of acceptance or rejection of the null fuzzy hypothesis is computed for each treatment of pollution. The data are from two plants: radish and cress, which are experimented on in soil polluted with CdNO3 salt. The results showed that using classical hypotheses Testing may lead to contradictory decisions, and the proposed fuzzy hypotheses Testing is a rational substitute for classical hypotheses Testing when the environment is in a vague status.

The problem of hypotheses Testing for a model of consisting from two independent objects is considered. It is assumed that five probability distributions are known and objects independently from each other follow one of them. In this paper using the theorem in [1] which Navaei has proved via the theory of large deviations the matrix of asymptotic inter-dependencies (reliability functions) of all possible pairs of the error probability exponents in optimal Testing for this model is determined. The case with two independent objects and two given probability distributions was researched by Haroutunian and Ahlswede.