Ononot — Consider a sequence of independent and identically distribut

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Inferential Statisticshard

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Consider a sequence of independent and identically distributed random variables $X_1, X_2, \dots, X_n$ with mean $\mu$ and variance $\sigma^2$ . If we define a test statistic $T_n = \frac{\bar{X}_n - \mu_0}{S_n / \sqrt{n}}$ , where $S_n$ is the sample standard deviation, what is the impact of the violation of the normality assumption on the distribution of $T_n$ as $n \to \infty$ ?