What assumption does a t-test require regarding the data?

The assumption that a t-test requires regarding the data includes the necessity for the data to exhibit normality of distribution. This means that, ideally, the data should follow a normal distribution pattern, especially in the case of smaller sample sizes. When the assumption of normality is met, it enhances the validity of the t-test results.

In practical application, if the sample size is large enough (typically n > 30), the Central Limit Theorem can imply that the sampling distribution of the sample mean will be approximately normal, even if the data itself is not perfectly normally distributed. However, for smaller sample sizes, strong deviations from normality can significantly affect the results, leading to incorrect conclusions.

This assumption is critical because the t-test relies on specific properties of the normal distribution to determine probabilities and confidence intervals. Therefore, confirming that the data meets this assumption is essential for the analysis to be accurate and reliable.

The other choices do not align with the fundamental assumptions of a t-test. For instance, while random sampling is important for ensuring the generalizability of results, it is not an exclusive assumption of the t-test itself. Additionally, although ordinal data can sometimes be analyzed, it does not satisfy the requirements for a t-test which is designed