Question

A data set lists earthquake depths. The summary statistics aren=600, overbarx=4.67 ​km, s=4.65 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 4.00. 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= 4.00km

H1​: μ> 4.00km

B.

H0​:μ= 4.00km

H1​: μ< 4.00km

C.

H0​: μ≠ 4.00km

H1​: μ= 4.00km

D.

H0​: μ= 4.00km

H1​: μ≠ 4.00km

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 (sufficient/not sufficient) evidence to conclude that the original claim that the mean of the population of earthquake depths is 4.00 km (is/is not correct).

Answer 1

a) The null and alternative hypothesis is ,

VS  

b) The test statistic is ,

c) Now , d.f.=Degrees of Freedom=n-1=600-1=599

The p-value is ,

p-value=

The Excel function is , =TDIST(3.53,599,2)

d) Decision : Here , p- value=0.000<0.01

Therefore , reject Ho

e) Conclusion : Reject H0. There is not sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 4.00 km