Question

A data set lists earthquake depths. The summary statistics are

Answer 1

Answer:

Step-by-step explanation:

The summary of the given statistics data include:

sample size n = 400

sample mean $\overline x$ = 6.86

standard deviation = 4.37

Level of significance ∝ = 0.01

Population Mean $\mu$ = 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 :

$H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00$

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

$z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}$

$z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}$

$z= \dfrac{0.86}{\dfrac{4.37}{20}}$

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 $H_o$ 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.