In the context of hypothesis testing, which of the following would be an appropriate null hypothesis?

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

Answer: (C)

Verified step by step guidance

1. Understand that in hypothesis testing, the null hypothesis (denoted as \(H_0\)) is a statement of no effect or no difference, and it usually includes an equality condition such as \(=\), \(\geq\), or \(\leq\).
2. Recognize that the null hypothesis is what you assume to be true before collecting evidence, and it is tested against the alternative hypothesis (\(H_a\)), which represents a change or difference.
3. Look at the options given: \(\mu > 50\), \(\mu < 50\), \(\mu = 50\), and \(\mu \neq 50\). The null hypothesis should be the statement that includes equality, so it can be tested directly.
4. Note that \(\mu = 50\) is the appropriate null hypothesis because it states a specific value for the population mean, which can be tested against alternatives like \(\mu > 50\) or \(\mu < 50\).
5. Conclude that the null hypothesis is typically written as \(H_0: \mu = 50\), while the alternative hypothesis would be \(H_a: \mu \neq 50\) (two-tailed) or \(H_a: \mu > 50\) or \(H_a: \mu < 50\) (one-tailed).