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.

In Testing hypotheses, we may confront with cases where data are recorded as non-precise (fuzzy) rather than crisp. In such situations, the classical methods of Testing hypotheses are not capable and need to be generalized. In solving the problem of Testing hypotheses based on fuzzy data, the fuzziness of the observed data leads to the fuzzy p-value. This paper has been focused to calculate fuzzy p-value based on fuzzy data using the extension principle. Also, considering that p-value method is the most widely used / popular approach for Testing hypotheses among different sciences users, two fuzzy p-value-based case studies have been provided in this paper. The first case study is discussed on “ the fuzzy data from a speedometer camera” and the second is deliberate about “ the lifetime of produced batteries in a factory” and both of them have been solved by a novel approach considering other studies found in the literature.

In this paper, a new approach is presented for Testing fuzzy hypotheses based on p-value method. In this method, we first formulate the hypotheses of interest by fuzzy sets, and then, the p-value is defined to integrate under the d-cuts of null fuzzy hypothesis. To compare the proposed p-value with the test significance level, we decide to accept or reject the null fuzzy hypothesis. Finally, the proposed method is employed by some numerical examples.

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.

This paper deals with the problem of Testing statistical hypotheses when the available data are fuzzy. In this approach, we first obtain a fuzzy test statistic based on fuzzy data, and then, based on a new signed distance between fuzzy numbers, we introduce a new decision rule to accept/reject the hypothesis of interest. The proposed approach is investigated for two cases: the case without nuisance parameters and the case with nuisance parameters. This method is employed to test the hypotheses for the mean of a normal distribution with known/unknown variance, the variance of a normal distribution, the difference of means of two normal distributions with known/unknown variances, and the ratio of variances of two normal distributions.

This paper reviews and compares two R packages “ FPV” and “ Fuzzy. p. value” . These packages are designed for Testing hypotheses in a fuzzy environment using a fuzzy p-value based approach. In fact, the packages “ FPV” and “ Fuzzy. p. value” propose some useful functions for Testing hypotheses when the data / hypotheses are fuzzy rather than crisp. The proposed methods and functions have been presented together with illustrative practical examples.