Which of the following is a prerequisite for using a Student-T test?

The prerequisite for using a Student-T test is that the data must be normally distributed. This is crucial because the Student-T test is designed to test the means of two groups when the data in each group follows a normal distribution. If the data is not normally distributed, the results of the T test may not be valid, potentially leading to incorrect conclusions.

In cases where the sample size is small, the assumption of normality becomes even more critical, as the Central Limit Theorem—which states that distributions of sample means will tend to be normal regardless of the shape of the population distribution—applies only as the sample size increases. Therefore, for small sample sizes, the normality assumption must be satisfied.

The other options do not pertain as prerequisites for the Student-T test. Nominal data does not provide a basis for calculating means, which is essential for this test. Ordinal data, while allowing for the calculation of medians, is not appropriate as it does not meet the requirement for interval or ratio-scale data necessary for mean analysis. Finally, while equal variance can be an important consideration in determining which version of the T test to use (pooled vs. unpooled), it is not a standalone prerequisite for using the test itself. Thus