I({\overline{X}_n})\equiv\left\{x \in R \quad | \quad \left(\overline{X}_n - \frac{\tilde{\sigma}_n}{\sqrt{n}}t(n-1, \alpha /2) < x < \overline{X}_n + \frac{\tilde{\sigma}_n}{\sqrt{n}}t(n-1, \alpha /2)\right)\right\}
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