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The relationship between the test of equality for two population means and the intersection of confidence intervals for the two means was developed in “Using Confidence Intervals to Test Hypotheses” by D. R. Barr in the October 1969 issue of JQT. In this paper an alternative procedure based on the best confidence region for (μ1,μ2) is developed. This alternative extends in a natural way for those cases when the standard deviation is unknown and/or the equality of more than two means is being tested.
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Jones et al. (1972) studied this question.
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