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Confidence Intervals for the Ratio of the Means of Two Normal Distributions with One Variance Unknown

: In this paper, we proposes confidence intervals for the ratio of normal means with one variance unknown based on the generalized confidence interval (GCI) approach, the method of variance estimates recovery (MOVER), and a Bootstrap technique (Bootstrap confidence interval (BCI). The coverage probabilities and expected lengths of these confidence intervals were then compared via a Monte Carlo simulation.The simulation results indicated that the MOVER approaches are satisfactory in terms of the coverage probability. The results indicate that the MOVER confidence intervals are better than those constructed via the GCI and BCI. The expected lengths of the MOVER approach are shorter than expected lengths of GCI and BCI. The coverage probabilities of the MOVER confidence intervals are more appropriate than those using the GCI and BCI. Simulation results show that the MOVER approach is satisfactory performances for all sample case which was presented by Thangjai et al. [19]. Our approaches are applied to an analysis of a real data set of drugs or treatments.