In this paper will be analyzed the application of the t-test against the nonparametric Mann - Whitney test in the analysis of health insurance benefit costs in the Republic of Srpska on large samples. This research aims to examine which method produces better results when testing statistical hypotheses. The adequacy of the statistical tests will be tested on primary health insurance cost data for 1,044,690 insureds in 2017. For two samples of size 4,000, the sampling distribution of the difference in two means has a skewness coefficient of 0.05 and a kurtosis coefficient of 3.09. Jarque - Bera test does not reject the hypothesis of normality of distribution with a p-value of 0.135. On the other hand, in the Mann - Whitney test, the real risk of the first species, when there is a difference in skewness between the samples, may be less than 0.001 compared to the nominal risk level of 0.05. Based on the results obtained, it is suggested to use the t-test instead of the Mann - Whitney test if the sample is large enough, which should be verified by the bootstrap method.
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 Blanchet J. & Lam H. (2013). A heavy traffic approach to modeling large life insurance portfolios. Insurance: Mathematics and Economics 53(1) 237-251. https://doi.org/10.1016/j.insmatheco.2013.04.011
 Chang H. J. Wu C. H.; Ho. J. F. Chen P. Y. (2008). On sample size for using Central limit theory in various distributions International Journal of Information and Management Sciences 19 (1).
 Cundill B. & Alexander N. D. (2015). Sample size calculations for skewed distributions. BMC medical research methodology 15(1) 28. https://doi.org/10.1186/s12874-015-0023-0
 Fagerland M. W. (2012). t-tests non-parametric tests and large studies—a paradox of statistical practice?. BMC Medical Research Methodology 12(1) 78.https://doi.org/10.1186/1471-2288-12-78
 Fagerland M. W. & Sandvik L. (2009). Performance of five two-sample location tests for skewed distributions with unequal variances. Contemporary clinical trials 30(5) 490-496. https://doi.org/10.1016/j.cct.2009.06.007
 Fagerland M. W. & Sandvik L. (2009). The wilcoxon–mann–whitney test under scrutiny. Statistics in medicine 28(10) 1487-1497. https://doi.org/10.1002/sim.3561
 Fay M. P. & Proschan M. A. (2010). Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. Statistics surveys 4 1. https://doi.org/10.1214/09-ss051
 Ловрић М.Комић Ј. & Стевић С. (2006). Статистичкаанализа: методи и примјена. Економски факултет Бања Лука Бања Лука(330-357).
 Lumley T. Diehr P. Emerson S. & Chen L. (2002). The importance of the normality assumption in large public health data sets. Annual review of public health 23(1) 151-169. https://doi.org/10.1146/annurev.publhealth.23.100901.140546
 Mann H. B. & Whitney D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The annals of mathematical statistics 50-60. https://doi.org/10.1214/aoms/1177730491
 Pandey R. M. (2015). Commonly used t-tests in medical research. Journal of the Practice of Cardiovascular Sciences 1(2) 185. https://doi.org/10.4103/2395-5414.166321
 Restrepo-Morales J. A. & Medina Hurtado S. (2012). Estimation of operative risk for fraud in the car insurance industry. Global Journal of Business Research 6(3) 73-83. https://doi.org/10.1002/9781118387047.ch6