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.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)