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

The p-value is 0.1867.

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 = (X - \mu)/((\sigma)/(√(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 = (X - \mu)/((\sigma)/(√(n)))`

`z = (66900 - 68000)/((5500)/(√(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.