In Estimating the Total of a Population of Size N $N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right]$

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In estimating the total of a population of size N, where N is very large compared to the sample size, the confidence interval estimator of the total is $N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right]$ .