When testing the difference of means for paired data, which of the following is the correct null hypothesis?

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

Answer: (C)

Verified step by step guidance

1. Understand that in hypothesis testing for paired data, we are interested in the mean difference \( \mu \) between the paired observations.
2. The null hypothesis \( H_0 \) typically states that there is no difference in means, which means the mean difference \( \mu \) is equal to zero.
3. Formally, the null hypothesis is written as: \[ H_0: \mu = 0 \]
4. The alternative hypothesis \( H_a \) can take different forms depending on the research question: it could be \( \mu \neq 0 \) (two-tailed), \( \mu > 0 \) (right-tailed), or \( \mu < 0 \) (left-tailed).
5. Therefore, the correct null hypothesis for testing the difference of means in paired data is that the mean difference is zero, which corresponds to \( H_0: \mu = 0 \).