Calibration of mean estimates is a crucial property in many applications, particularly in actuarial decision-making. Tests of mean-calibration are often performed under the assumption that the estimated means correctly preserve the ordering of the corresponding population means. In this paper, we first consider the classical Likelihood Ratio Test (LRT) within the Exponential Dispersion Family (EDF), and we show that applying likelihood-based methods to test mean-calibration within the EDF requires a strong ordering assumption on the mean estimates. This assumption makes the null hypothesis of the mean-calibration test equivalent to the correct specification of the mean estimates. Next, we investigate the framework of universal inference for testing mean-calibration and mean-specification, and the relationship between the tests. We develop a sub-sampled split LRT within the EDF that provides finite-sample guarantees with universally valid critical values. We investigate type I error, power, and e-power of the sub-sampled split LRT and compare its performance with that of the classical LRT. We also propose a novel test statistic based on a sub-sampled split $L_q$-likelihood ratio test (L$q$RT) to enhance the performance of the statistical test. Numerical results demonstrate that universal inference based on the sub-sampled split LRT and sub-sampled split L$q$RT provides an attractive alternative to the classical LRT within the EDF, achieving high power for detecting miscalibration and misspecification in medium- and large-sized samples.

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