Problem

The statement represents a claim. Write its complement and state which is $\mathrm{H}_{0}$ and which is $\mathrm{H}_{\mathrm{A}}$.
$\mu=8.3$
A. $H_{0}: \mu=8.3$ (claim); $H_{a}: \mu \neq 8.3$
B. $H_{0}: \mu \neq 8.3 ; H_{a}: \mu=8.3$ (claim)
C. $H_{0}: \mu \geq 8.3$ (claim); $H_{a}: \mu< 8.3$
D. $H_{0}: \mu \leq 8.3 ; H_{a}: \mu> 8.3$ (claim)

Answer

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Answer

Final Answer: \(\boxed{A. H_{0}: \mu=8.3 \text{ (claim); } H_{a}: \mu \neq 8.3}\)

Steps

Step 1 :The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{A}$. The claim is that $\mu=8.3$.

Step 2 :The null hypothesis ($H_{0}$) is usually a statement of no effect or no difference. It is the hypothesis that the researcher is trying to disprove.

Step 3 :The alternative hypothesis ($H_{A}$) is a statement that contradicts the null hypothesis. It is what the researcher believes to be true and is trying to prove.

Step 4 :In this case, the claim is that $\mu=8.3$. This would be our null hypothesis.

Step 5 :The complement of this claim, which would be our alternative hypothesis, is that $\mu \neq 8.3$.

Step 6 :Final Answer: \(\boxed{A. H_{0}: \mu=8.3 \text{ (claim); } H_{a}: \mu \neq 8.3}\)

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