A new confidence interval for the ratio of two normal means and comparisons

The problem of estimating the ratio of means of two independent normal distributions is considered. Interval estimation method similar to Welch's approximate degrees of freedom solution for the Behrens-Fisher problem is proposed. The test and confidence interval (CI) for the ratio of means are compared with the available CIs including the one based on the modified likelihood ratio test. Extensive simulation studies indicate that the proposed method is accurate even for very small samples and simpler than other available likelihood-based tests and CIs. The methods are illustrated using an example.