When testing the difference of means for paired data, what is the null hypothesis?

• A. $\mu \ne 0$
• B. $\mu =0$
• C. $\mu >0$
• D. $\mu <0$

Answer: (B)

Verified step by step guidance

1. Understand that in paired data tests, we are interested in the mean difference \( \mu_d \) between the paired observations.
2. The null hypothesis \( H_0 \) typically states that there is no difference in means, which means the mean difference is zero: \( H_0: \mu_d = 0 \).
3. The alternative hypothesis \( H_a \) can take different forms depending on the research question: it could be \( \mu_d \neq 0 \) (two-tailed), \( \mu_d > 0 \) (right-tailed), or \( \mu_d < 0 \) (left-tailed).
4. Since the question asks specifically for the null hypothesis, focus on the statement that the mean difference equals zero, indicating no effect or no change.
5. Therefore, the null hypothesis for testing the difference of means in paired data is \( \mu_d = 0 \).