Which of the following is an assumption required to use the two-sample test of means ($t$-test for independent samples)?

• A. The populations from which the samples are drawn are normally distributed.
• B. The data must be measured on a nominal scale.
• C. The two samples are independent of each other.
• D. The two samples must have equal sample sizes.

Answer: (C)

Verified step by step guidance

1. Understand that the two-sample t-test for means (independent samples t-test) is used to compare the means of two independent groups to see if there is a statistically significant difference between them.
2. Recall the key assumptions required for the independent samples t-test: (1) The two samples are independent of each other, (2) The populations from which the samples are drawn are approximately normally distributed, and (3) The variances of the two populations are equal (homogeneity of variance).
3. Note that the data must be measured on at least an interval or ratio scale, not a nominal scale, because the t-test compares means, which require numerical data.
4. Recognize that equal sample sizes are not a strict requirement for the independent samples t-test; the test can handle unequal sample sizes, although equal sizes can improve robustness.
5. Therefore, among the options given, the assumption that 'The two samples are independent of each other' is a fundamental requirement to validly perform the two-sample t-test.