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

Step-by-step explanation:

The summary of the given statistics data include:

sample size n = 400

sample mean = 6.86

standard deviation = 4.37

Level of significance ∝ = 0.01

Population Mean = 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.

To start with the hypothesis;

The null and the alternative hypothesis can be computed as :

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

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 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.

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

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1. 34

2. 268

3. x=14.4

step-by-step explanation: