A data set lists earthquake depths. The summary statistics are $n=600$, $\bar{x}=6.38 \mathrm{~km}, \mathrm{~s}=4.69 \mathrm{~km}$. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00 . Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
\[
\begin{array}{l}
H_{0}: \mu=6.00 \mathrm{~km} \\
H_{1}: \mu \neq 6.00 \mathrm{~km}
\end{array}
\]
C.
\[
\begin{array}{l}
H_{0}: \mu=6.00 \mathrm{~km} \\
H_{1}: \mu> 6.00 \mathrm{~km}
\end{array}
\]
B. $H_{0}: \mu=6.00 \mathrm{~km}$ $H_{1}: \mu< 6.00 \mathrm{~km}$
D.
\[
\begin{array}{l}
H_{0}: \mu \neq 6.00 \mathrm{~km} \\
H_{1}: \mu=6.00 \mathrm{~km}
\end{array}
\]
Answer
So, the final answer is \(\boxed{\begin{array}{l}H_{0}: \mu=6.00 \mathrm{~km} \ H_{1}: \mu \neq 6.00 \mathrm{~km}\end{array}}\).
Step 1 ：The null hypothesis is typically a statement of no effect or no difference. In this case, the null hypothesis would be that the mean earthquake depth is equal to 6.00 km.
Step 2 ：The alternative hypothesis is what we are testing against the null hypothesis. In this case, since the question does not specify a direction (greater than or less than), the alternative hypothesis would be that the mean earthquake depth is not equal to 6.00 km.
Step 3 ：Therefore, the null and alternative hypotheses are as follows: \(H_{0}: \mu=6.00 \mathrm{~km}\) and \(H_{1}: \mu \neq 6.00 \mathrm{~km}\)
Step 4 ：So, the final answer is \(\boxed{\begin{array}{l}H_{0}: \mu=6.00 \mathrm{~km} \ H_{1}: \mu \neq 6.00 \mathrm{~km}\end{array}}\).
