Question

A data set lists earthquake depths. The summary statistics are n=600​, x=6.64 ​km, s=4.23 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?

Answer 1

Since n is very large, we use the z distribution.

Given: = 6, = 6.64, s = 4.23, n = 600, = 0.01

The Hypothesis:

H0: = 6 (Claim)

Ha: 6

The Test Statistic: The test statistic is given by the equation:

Z observed = 3.71

The p Value: The p value, 2 tailed for Z = 3.71, p value = 0.0002

This p value indicates the probability of getting a test statistic as extreme as or greater than that which has been obtained under the assumption/condition that the null hypothesis is true.

The Decision Rule: If P value is < , Then Reject H0.

The Decision: Since P value (0.0002) is < (0.01) , We Reject H0.

The Conclusion: There is sufficient evidence at the 99% significance level to warrant rejection of the claim that the earthquakes are from a population whose mean is equal to 6.