A data set lists earthquake depths. The summary statistics are n =500 , x =6.78km, s= 4.41 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?
A. H0 : μ ≠ 6.00km H1 : μ = 6.00km
B. H0 : μ =6.00km H1 : μ >6.00km
C. H0 : μ =6.00km H1 : μ <6.00km
D. H0 : μ =6.00km H1 : μ ≠ 6.00km
Determine the test statistic.
(Round to two decimal places as needed.)
Determine the P-value.
(Round to three decimal places as needed.)
State the final conclusion that addresses the original claim.
▼ Reject Fail to reject
H0.
There is
▼ not sufficient sufficient
evidence to conclude that the original claim that the mean of the population of earthquake depths is 6.00km
▼is not is correct.
To Test :-
D. H0 : μ =6.00km
H1 : μ ≠ 6.00km
Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 6.78 - 6 ) / ( 4.41 / √(500) )
t = 3.96
Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
t(α/2, n-1) = t(0.01 /2, 500-1) = 2.586
| t | > t(α/2, n-1) = 3.955 > 2.586
Result :- Reject null hypothesis
Decision based on P value
P - value = P ( t > 3.955 ) = 0.0001
Reject null hypothesis if P value < α = 0.01 level of
significance
P - value = 0.0001 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis
There is not sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 6.00 km.
A data set lists earthquake depths. The summary statistics are n =500 , x =6.78km, s=...
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