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 $N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right]$ .

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This is true. The confidence interval estimator of the total of a population is given by the formula N[ x̄ ± tα/2 ⋅ s/√n], where N is the size of the population, x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value corresponding to the desired level of confidence and degree of freedom. Since N is much larger than n, the effect of the sample size on the accuracy of the estimate is negligible.

In Estimating the Total of a Population of Size N,where N[xˉ±tα/2⋅s/n]N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right]N[xˉ±tα/2​⋅s/n​]

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