Question

A data set lists earthquake depths. The summary statistics are n=600​, x=6.41 ​km, s=4.84 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

n = 600, = 6.41 km and s = 4.84 km

Here significane level = 0.01

Here we have to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00.

HYpothesis are

H₀ : = 6.00

H_a : 6.00

standard error of sample mean = se = s/sqrt(N) = 4.84/sqrt(600) = 0.1976 km

As population standard deviation is not given so we should use t distribution but as sample size is too high so we can approximate the t distribution to Z distribution.

Critical value for alpha = 0.01 is

Z_critical = 2.575

Z = ( - ₀)/se = (6.41 - 6.00)/0.1976 = 2.075

P - value = 2 * NORMSDIST(Z = 2.075) = 0.0380 > 0.01

so here Z < Z_critical so we would fail to to reject the null hypothesis so we would conclude that earthquakes are from a population with a mean equal to 6.00.