Question

A data set lists earthquake depths. The summary statistics are n=500​, x bar=6.78 ​km, s=4.44 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

Solution :

Given that,

Population mean = = 6

Sample mean = = 6.78

Sample standard deviation = s = 4.44

Sample size = n = 500

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 6

Ha: 6

The test statistics,

t = ( - )/ (s/)

= ( 6.78 - 6 ) / ( 4.44 /500 )

= 3.928

P- Value = 0.0001   

The p-value is p = 0.0001 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is not enough evidence to support the claim that of a seismologist that these earthquakes are from a population with a mean equal to 6.00, at the 0.01 significance level.