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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 4.1 pounds/square inch (psi). Assume the population standard deviation is 0.6. The engineer designed the valve such that it would produce a mean pressure of 4.2 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.

Respuesta :

ajeigbeibraheem

Answer:

P-value = 0.0046  

Step-by-step explanation:

Given that:

Sample size n = 290

sample mean [tex]\overline{x_1}[/tex] = 4.1

standard deviation [tex]\sigma[/tex] = 0.6

population mean [tex]\mu[/tex] = 4.2

The null and the alternative hypothesis

[tex]\mathbf{H_o: \mu = 4.2} \\ \\ \mathbf{H_a: \mu \ne 4.2}[/tex]

This is a two-tailed test.

The test statistics can be computed as:

[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{4.1 - 4.2 }{\dfrac{0.6}{\sqrt{290}}}[/tex]

[tex]Z = \dfrac{-0.1 }{\dfrac{0.6}{\sqrt{290}}}[/tex]

Z = -2.838

P-value = P(Z> 2.838)

P-value = P(Z< -2.838) +P(Z > 2.838)

P-value = 0.00227 + (1 - 0.9977)

P-value = 0.00457

P-value = 0.0046      (to 4 decimal places)

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