Which statement is an assumption of the two-sample t-test?

Which statement is an assumption of the two-sample t-test?

• A. Two samples are randomly selected
• B. The samples are drawn from non-normal populations
• C. The dependent variable is nominal
• D. The grouping variable has more than two categories

Answer: (A)

The main idea is that the two-sample t-test relies on sampling assumptions that let us generalize the results to the population. Having two samples randomly selected supports this by promoting independence and representativeness, which are essential for comparing the two group means meaningfully. If the populations were clearly non-normal, the test would not be meeting its typical normality-related assumption, and with small samples this would be problematic. The dependent variable should be measured on a continuous scale, not nominal, because the t-test compares means. And the grouping variable should have exactly two groups; with more than two categories you’d need a different approach (like ANOVA). So random selection of the two samples best captures the required assumption, supporting valid inference about the population means.

The main idea is that the two-sample t-test relies on sampling assumptions that let us generalize the results to the population. Having two samples randomly selected supports this by promoting independence and representativeness, which are essential for comparing the two group means meaningfully.

If the populations were clearly non-normal, the test would not be meeting its typical normality-related assumption, and with small samples this would be problematic. The dependent variable should be measured on a continuous scale, not nominal, because the t-test compares means. And the grouping variable should have exactly two groups; with more than two categories you’d need a different approach (like ANOVA).

So random selection of the two samples best captures the required assumption, supporting valid inference about the population means.