Which of the following is an appropriate null hypothesis for the student's experiment?

• A. $H:\mu <0$ (The population mean is less than zero)
• B. $H:\mu \ne 0$ (The population mean is not equal to zero)
• C. $H:\mu >0$ (The population mean is greater than zero)
• D. $H:\mu =0$ (The population mean is equal to zero)

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, which serves as the starting assumption for hypothesis testing.
2. Recognize that the null hypothesis typically includes an equality, such as \(\mu = 0\), where \(\mu\) represents the population mean.
3. Identify that alternative hypotheses (denoted as \(H_a\) or \(H_1\)) express the research question and usually involve inequalities like \(\mu \neq 0\), \(\mu < 0\), or \(\mu > 0\).
4. Review the options given and note that hypotheses stating \(\mu < 0\), \(\mu \neq 0\), or \(\mu > 0\) are alternative hypotheses, not null hypotheses.
5. Conclude that the appropriate null hypothesis is the one stating \(H_0: \mu = 0\), which assumes no difference or effect until evidence suggests otherwise.