Which of the following would be an appropriate null hypothesis in a hypothesis testing scenario?

• A. $\mu <50$
• B. $\mu \ne 50$
• C. $\mu >50$
• D. $\mu =50$

Answer: (D)

Verified step by step guidance

1. Understand that the null hypothesis (denoted as \(H_0\)) is a statement of no effect or no difference, and it usually includes an equality (e.g., \(=\)) to represent the status quo or a baseline value.
2. Review the options given: \(\mu < 50\), \(\mu \neq 50\), and \(\mu > 50\) are all alternative hypotheses because they suggest the mean is different from 50 in some way.
3. Recognize that the null hypothesis should be the complement of the alternative hypothesis and typically states that the population mean \(\mu\) is equal to a specific value, in this case, 50.
4. Formulate the null hypothesis as \(H_0: \mu = 50\), which means the population mean is equal to 50, serving as the baseline assumption to be tested against.
5. Remember that during hypothesis testing, you either reject or fail to reject the null hypothesis based on the evidence from the sample data.