Which of the following hypotheses is not an appropriate form for an alternative hypothesis in hypothesis testing?

• A. $H:\mu >10$
• B. $H:\mu <10$
• C. $H:\mu \ne 10$
• D. $H:\mu =10$

Answer: (D)

Verified step by step guidance

1. Understand that in hypothesis testing, the alternative hypothesis (denoted as \(H_1\) or \(H_a\)) represents what we want to test or find evidence for, and it must be a statement that contradicts the null hypothesis (\(H_0\)).
2. Recall that the null hypothesis (\(H_0\)) is usually a statement of equality, such as \(H_0: \mu = 10\), which assumes no effect or no difference.
3. Recognize that the alternative hypothesis should be an inequality or difference, such as \(H_a: \mu > 10\), \(H_a: \mu < 10\), or \(H_a: \mu \neq 10\), because it expresses the possibility that the parameter is different from the null value.
4. Note that an alternative hypothesis of the form \(H_a: \mu = 10\) is not appropriate because it is identical to the null hypothesis and does not represent a competing claim to test against.
5. Therefore, the alternative hypothesis must always be a statement that challenges the null hypothesis by using inequalities (\(>\), \(<\)) or not equal (\(\neq\)), and never an equality.