Two kinds of sequential procedures are proposed for the construction of fixed-width confidence intervals for the common mean of several normal populations. The first kind is motivated by the solution of the fixed-sample problem with known variances. Thus a sequential procedure is obtained which takes an observation from each population at each stage. The second kind of procedure, which could lead to a considerable savings in observations, first uses a procedure for the selection of the smallest variance. Further observations are then taken only from the selected population. Asymptotic properties and asymptotic relative efficiencies are investigated. Results of a Monte Carlo study indicate agreement between the asymptotic results and the actual behavior of the procedures.
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