# Testing Statistical Hypotheses Based on Fuzzy Confidence Intervals

### Abstract

A fuzzy test for testing statistical hypotheses about an imprecise parameter is proposed for the case when the available data are also imprecise. The proposed method is based on the relationship between the acceptance region of statistical tests at level β and confidence intervals for the parameter of interest at confidence level 1 − β. First, a fuzzy confidence interval is constructed for the fuzzy parameter of interest. Then, using such a fuzzy confidence interval, a fuzzy test function is constructed. The obtained fuzzy

test, contrary to the classical approach, leads not to a binary decision (i.e. to reject or to accept the given null hypothesis) but to a fuzzy decision showing the degrees of acceptability of the null and alternative hypotheses. Numerical examples are given to demonstrate the theoretical results, and show the

possible applications in testing hypotheses based on fuzzy observations.

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*Austrian Journal of Statistics*,

*41*(4), 267–286. https://doi.org/https://doi.org/10.17713/ajs.v41i4.168

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