Question

A data set lists earthquake depths. The summary statistics are nequals300​, x overbarequals5.89 ​km, sequals4.44 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 5.00. 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.

Answer 1

Answer:

Null hypothesis $H_0:\mu=5.00km$

Alternative hypothesis $H_1:\mu\neq 5.00km$

The p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

Step-by-step explanation:

It is given that a data set lists earthquake depths. The summary statistics are

$n=300$

$\overline{x}=5.89km$

$s=4.44km$

Level of significance = 0.01

We need to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00.

Null hypothesis $H_0:\mu=5.00km$

Alternative hypothesis $H_1:\mu\neq 5.00km$

The formula for z-value is

$z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}$

$z=\frac{5.89-5.00}{\frac{4.44}{\sqrt{300}}}$

$z=\frac{0.89}{0.25634351952}$

$z=3.4719$

The p-value for z=3.4719 is 0.000517.

Since the p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.