A data set lists earthquake depths. The summary statistics are n$=400,$ x$=5\mathrm{.}43$km$,$ s$=4\mathrm{.}45$ km$.$ Use a $0\mathrm{.}01$ significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to $5\mathrm{.}00.$ 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.