Exact Confidence Intervals for the Common Mean of Several Normal Populations
The problem of interval estimation of the common mean of several normal populations when the variances are unknown and unequal is considered. Some new confidence intervals are proposed. One of them is centered at the well- known Graybill-Deal estimator of the common mean. These new intervals and an existing exact confidence interval are numerically compared with respect to their expected lengths. Based on comparison studies, some recommendations are made regarding the choice of the intervals to be used in applications.
Jordan, S. M., & Krishnamoorthy, K. (1996). Exact Confidence Intervals for the Common Mean of Several Normal Populations. Biometrics, 52(1), 77–86. https://doi.org/10.2307/2533146