… In this paper we address the problem of constructing exact confidence intervals for μ
based on several pivots and combinations of appropriately defined P-values, and compare
them with some existing results based on their expected lengths. … Here again we have
applied all the techniques described in Section 4, and computed the two-sided confidence
intervals for the common mean μ with α=0.05. We have also included intervals based on
Sinha (1985) and Meier (1953), using simulated cut-off points (assuming the true variances …

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.