Question

A data set lists earthquake depths. The summary statistics are nequals600​, x overbarequals4.39 ​km, sequals4.65 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 4.00. 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. Upper H 0​: munot equals4.00 km Upper H 1​: muequals4.00 km B. Upper H 0​: muequals4.00 km Upper H 1​: munot equals4.00 km C. Upper H 0​: muequals4.00 km Upper H 1​: muless than4.00 km D. Upper H 0​: muequals4.00 km Upper H 1​: mugreater than4.00 km Determine the test statistic. 2.05 ​(Round to two decimal places as​ needed.) Determine the​ P-value. nothing ​(Round to three decimal places as​ needed.) State the final conclusion that addresses the original claim. ▼ Fail to reject Reject Upper H 0. There is ▼ sufficient not sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 4.00 km ▼ is is not correct.

Answer 1

Null Hypothesis, 4

Alternative Hypothesis, 4

xbar = 4.39
s = 4.65
n = 600

Test statistic,

t = (4.39 - 4)/(4.65/sqrt(600))
t = 2.05

This is two tailed test
p-value = 2*P(t > 2.05)
p-value = 0.0408

As p-value > 0.01, fail to reject H0
There is not sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 4.00 km is not correct.