The t-test is strictly appropriate for tests involving sample sizes larger than 30 with known standard deviations.

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Quizplus · Accepted Answer

The t-test can be used for sample sizes larger than 30 regardless of whether the standard deviation is known or unknown. If the population standard deviation is unknown, then the sample standard deviation is used as an estimate in the calculation. For sample sizes smaller than 30, the t-test is appropriate as long as the population has a normal distribution or the sample size is sufficiently large (i.e. greater than or equal to 10) and the data is approximately normally distributed.

The T-Test Is Strictly Appropriate for Tests Involving Sample Sizes