Recall the Conditions for a t-test:

• If the data is comes from a normal distribution, then the t-test and the confidence interval are exact.
• If the data doesn’t come from a normal distribution, then the t-test and confidence interval will be approximate if
• n < 15 and the data are close to normal. If the data are clearly not normally distributed or outliers exist, do not use the t-test.
• n ≥ 15, then the t-tests can be used except in the case that the data contains outliers or the data is strongly skewed.
• n ≥ 40 (large samples), then the t-tests can be used even for skewed distributions and the results will be approximate but fairly accurate.