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

• A. $H{a}_1:\mu >10$
• B. $H{a}_3:\mu =10$
• C. $H{a}_4:\mu <10$
• D. $H{a}_2:\mu \ne 10$

Answer: (B)

Verified step by step guidance

1. Understand that in hypothesis testing, the alternative hypothesis (denoted as \(H_a\)) represents what we want to test for and must be a statement that contradicts the null hypothesis (\(H_0\)).
2. Recall that the null hypothesis typically includes an equality (e.g., \(\mu = 10\)), and the alternative hypothesis should be an inequality or difference (e.g., \(\mu > 10\), \(\mu < 10\), or \(\mu \neq 10\)).
3. Identify that an alternative hypothesis stating \(\mu = 10\) is not appropriate because it is an equality, which belongs to the null hypothesis, not the alternative.
4. Review the given options and recognize that \(H_a: \mu = 10\) is the incorrect form for an alternative hypothesis since it does not contradict the null hypothesis but rather repeats the equality.
5. Conclude that valid alternative hypotheses must express a difference or inequality, such as \(\mu > 10\), \(\mu < 10\), or \(\mu \neq 10\), to properly test against the null hypothesis.