Question

A data set lists earthquake depths. The summary statistics are

n=400​

x =6.73 km

s=4.13 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

H0: = 6

Ha: 6

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 6.73 - 6 ) / ( 4.13 / √(400) )
t = 3.54

With test statistics of 3.54 and df of 399,

P - value = 0.0004   
Reject null hypothesis if P value < α = 0.01 level of significance      
P - value = 0.0004 < 0.01 ,hence we reject null hypothesis      
Conclusion :-

We have sufficient evidence to support the claim that earthquakes are from a population

with a mean equal to 6.00