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Sagot :
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:
[tex]H_0: \mu = 68000[/tex]
At the alternate hypothesis, we test that it is more than 68000. So
[tex]H_a: \mu > 68000[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
68000 is tested at the null hypothesis:
This means that [tex]\mu = 68000[/tex]
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 [tex]n = 20, X = 66900, \sigma = 5500[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{66900 - 68000}{\frac{5500}{\sqrt{20}}}[/tex]
[tex]z = -0.89[/tex]
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.
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