A data set lists earthquake depths. The summary statistics are
nequals=400400,
x overbarxequals=6.866.86
km,
sequals=4.374.37
km. Use a
0.010.01
significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to
6.006.00.
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.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμnot equals≠5.005.00
km

B.
Upper H 0H0:
muμnot equals≠5.005.00
km
Upper H 1H1:
muμequals=5.005.00
km

C.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμgreater than>5.005.00
km

D.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμless than<5.005.00
km
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.

Fail to reject

Upper H 0H0.
There is

evidence to conclude that the original claim that the mean of the population of earthquake depths is
5.005.00
km

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.

To start with the hypothesis;

The null and the alternative hypothesis can be computed as :

[tex]H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00[/tex]

The test statistics for this two tailed test can be computed as:

[tex]z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}[/tex]

[tex]z= \dfrac{0.86}{\dfrac{4.37}{20}}[/tex]

z = 3.936

degree of freedom = n - 1

degree of freedom = 400 - 1

degree of freedom = 399

At the level of significance ∝ = 0.01

P -value = 2 × (z < 3.936) since it is a two tailed test

P -value = 2 × ( 1 - P(z ≤ 3.936)

P -value = 2 × ( 1 -0.9999)

P -value = 2 × ( 0.0001)

P -value = 0.0002

Since the P-value is less than level of significance , we reject [tex]H_o[/tex] at level of significance 0.01

Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 5.00 km.