Question

Calculate the P-value for the given scenario. Use 4 decimal places.:
Employees at a construction and mining company claim that the mean salary of the company's mechanical engineers is less than that of the one
of its competitors, which is $68,000. A random sample of 20 of the company's mechanical engineers has a mean salary of $66,900. Assume the
population standard deviation is $5500 and the population is normally distributed.

Answer 1

Answer:

The p-value is 0.1867.

Step-by-step explanation:

Employees at a construction and mining company claim that the mean salary of the company's mechanical engineers is less than that of the one of its competitors, which is $68,000.

At the null hypothesis we test that the salary is the same of the competitor, that is:

$H_0: \mu = 68000$

At the alternate hypothesis, we test that it is more than 68000. So

$H_a: \mu > 68000$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

68000 is tested at the null hypothesis:

This means that $\mu = 68000$

A random sample of 20 of the company's mechanical engineers has a mean salary of $66,900. Assume the population standard deviation is $5500.

This means that $n = 20, X = 66900, \sigma = 5500$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{66900 - 68000}{\frac{5500}{\sqrt{20}}}$

$z = -0.89$

P-value:

The pvalue is the probability of finding a sample mean below 66900, which is the pvalue of z = -0.89.

Looking at the z-table, z = -0.89 has a pvalue of 0.1867.

The p-value is 0.1867.