Statisticians have discovered that the one-sample t test is not robust to violations of the normality assumption under any conditions.

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Quizplus · Accepted Answer

The one-sample t test is actually quite robust to violations of the normality assumption, as long as the sample size is large enough (typically at least 30). In fact, even with smaller sample sizes, the t test can still perform reasonably well if the data are not highly skewed or have extreme outliers. However, there are alternative tests (e.g. Wilcoxon signed-rank test) that are more appropriate for non-normal data.

Statisticians Have Discovered That the One-Sample T Test Is Not