Which of the following is NOT an assumption of the paired-samples $t$ test?

• A. The pairs are randomly and independently selected from the population.
• B. The differences between paired observations are normally distributed.
• C. The two samples are independent of each other.
• D. The measurement scale of the data is interval or ratio.

Answer: (C)

Verified step by step guidance

1. Understand that the paired-samples t test is used to compare two related groups, such as measurements before and after a treatment on the same subjects.
2. Recall the key assumptions of the paired-samples t test: (1) the pairs are randomly and independently selected from the population, (2) the differences between paired observations are normally distributed, and (3) the measurement scale of the data is interval or ratio.
3. Recognize that the assumption about independence applies to the pairs themselves, not to the two samples being independent of each other, because the test specifically deals with related or paired samples.
4. Identify that the statement 'The two samples are independent of each other' contradicts the fundamental nature of the paired-samples t test, which requires dependent (paired) samples.
5. Conclude that the statement 'The two samples are independent of each other' is NOT an assumption of the paired-samples t test.