Question

A data set lists earthquake depths. The summary statistics are n=500, x =5.77 km, s=4.69 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 5.00. 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

H0: = 5

Ha: 5

Test statistics

t = - / S / sqrt(n)

= 5.77 - 5 / 4.69 / sqrt(500)

= 3.67

This is test statistics value.

df = n -1 = 500 - 1 = 499

From the T table,

p-value at test statistics t = 3.67 and df = 499 is 0.0003

Since p-value < 0.01 level, we have sufficient evidence to reject the null hypothesis.

We conclude at 0.01 level that we have sufficient evidence to support the claim.