Test the claim about the population mean, $\mu$, at the given level of significance using the given sample statistics.
Claim: $\mu \neq 7000 ; \alpha=0.02, \sigma=369$. Sample statistics: $\bar{x}=6600, n=44$
Identify the null and alternative hypotheses. Choose the correct answer below.
A. $\mathrm{H}_{0}, \mu \neq 7000$
\[
H_{a} \mu \geq 7000
\]
C.
\[
\begin{array}{l}
H_{0}: \mu \leq 7000 \\
H_{a} \mu \neq 7000
\end{array}
\]
E. $\mathrm{H}_{0}: \mu \geq 7000$
\[
H_{a} \cdot \mu \neq 7000
\]
B. $\mathrm{H}_{0} \mu \neq 7000$
\[
H_{a} \cdot \mu \leq 7000
\]
D.
\[
\begin{array}{l}
H_{0} \cdot \mu=7000 \\
H_{a} \cdot \mu \neq 7000
\end{array}
\]
F.
\[
\begin{array}{l}
H_{0}: \mu \neq 7000 \\
H_{a}: \mu=7000
\end{array}
\]
Answer
Final Answer: \(\boxed{\begin{array}{l} H_{0}: \mu=7000 \\ H_{a}: \mu \neq 7000 \end{array}}\)
Step 1 ：Identify the null and alternative hypotheses. The null hypothesis is usually a statement of no effect or no difference. It is the hypothesis that the researcher is trying to disprove. In this case, the null hypothesis would be that the population mean is equal to 7000. The alternative hypothesis is what you might believe to be true or hope to prove true. In this case, the alternative hypothesis would be that the population mean is not equal to 7000.
Step 2 ：Choose the correct answer from the given options. The correct answer is D. \(H_{0}: \mu=7000\) and \(H_{a}: \mu \neq 7000\)
Step 3 ：Final Answer: \(\boxed{\begin{array}{l} H_{0}: \mu=7000 \\ H_{a}: \mu \neq 7000 \end{array}}\)
