This paper addresses the problem of hypothesis test on response mean with various inequality constraints in the presence of covariates when response data are missing at random. The various hypotheses include to test single point, two points, set of inequalities as well as two-sided set of inequalities of the response mean. The test statistics is constructed by the weighted-corrected empirical likelihood function of the response mean based on the approach of weighted-corrected imputation for the response variable. We investigate limiting distributions and asymptotic powers of the proposed empirical likelihood ratio test statistics with auxiliary information. The results show that the test statistics with auxiliary information is more efficient than that without auxiliary information. A simulation study is undertaken to investigate the finite sample performance of the proposed method.