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 \(\boxed{\begin{array}{l}H_{0}: \mu=6.00 \mathrm{~km} \ H_{1}: \mu \neq 6.00 \mathrm{~km}\end{array}}\).