Question

A data set lists earthquake depths. The summary statistics are n=600, x̅=6.68 km, s=4.55 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.

Answer 1

$\\Given,\\ Level~of~significance(\alpha)=0.01\\\\ sample~Size(n)=600\\\\ Standard~Deviation(s)=4.55\\\\ Sample~Mean(\bar{x})=6.68\\\\ .....................................................\\ Null~Hypothesis~H_0:\mu=6\\\\ Alternative~Hypothesis~H_1:\mu \neq 6\\\\ Ans:C.) ........................................................\\ Test~Statistic(t)=\frac{\bar{x}-\mu}{s/\sqrt{n}}=\frac{6.68-6}{4.55/\sqrt{600}}=3.66\\\\ .........................................................\\ Degree~of~freedom=n-1=600-1=599\\ P-value=P(|t|>3.66)\\\\ ~~~~~~=0 .0003\\\\ (use~excel~function:==TDIST(3.66,599,2)\\\\ ............................................................\\\\ as~p-value~is~less~than significance~level(\alpha=0.01), ~Reject~Null~Hypothesis.\\\\ ............................................................\\ Conclusion:Hence, ~there~is~Enough~evidence~to~support~the~claim.$