A Simple Confidence interval for the difference of two normal population means with one variance unknown

Abstract

In this paper, asymptotic coverage probabilities and expected lengths of confidence intervals for the difference between the means of two normal populations with one variance unknown are derived. Monte Carlo simulations results indicate that our proposed confidence interval, which is easy to use, performs as well as the existing confidence intervals.Keywords: confidence interval, coverage probability, expected length, normal means. IntroductionRecently, confidence intervals for the difference between two normal population means have been investigated. it is known that a confidence interval based on the t-distribution with pooled sample variances is preferable when it is assumed that two population variances are equal; otherwise, the Welch-Satterthwaite (WS, hereafter) confidence interval is preferable, see e.g. biased estimator of the number of degrees of freedom. Hence, they proposed an unbiased degrees of freedom of the t-test statistic which is described in section 2.2. Peng and Tong [9] showed that the t-test statistic with the unbiased estimator of the number of degrees of freedom 3  performs better that that of the Maity and Sherman's method especially when the variance of the unknown variance is large. In practice, both test statistics, however, need time to compute the number of degrees of freedom. In this paper, we therefore, propose a simple and easy method to construct the confidence interval with one variance unknown as in Niwitpong [10]. We also proved the coverage probability and the expected length of each confidence interval in comparison with the WS confidence interval. The paper is organized as follows. Section 2 presents confidence intervals for the difference between two normal population means with one variance unknown. Coverage probabilities and expected lengths of confidence intervals in section 2 are derived in section 3. Section 4 contains a discussion of the results and conclusions.