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Exact confidence intervals for the common mean of several normal populations. (English) Zbl 0877.62032
Summary: 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 F. A. Graybill and R. B. Deal estimator [Biometrics 15, 543-550 (1959; Zbl 0096.34503)] 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.

MSC:
62F25 Parametric tolerance and confidence regions
62P10 Applications of statistics to biology and medical sciences; meta analysis
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