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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 5.4 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 5.5 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.

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JeanaShupp

Answer: -1.77

Step-by-step explanation:

Let [tex]\mu[/tex] be the population mean.

Given : The engineer designed the valve such that it would produce a mean pressure of 5.5 psi.  It is believed that the valve does not perform to the specifications.

Then , [tex]H_0:\mu=5.5[/tex]

[tex]H_1:\mu\neq5.5[/tex]

Since , the alternative hypothesis is two-tailed , so the test is a two tailed test.

Also. sample size : [tex]n=200[/tex]

Sample mean : [tex]\overline{x}=5.4[/tex]

[tex]\sigma=0.8[/tex]

Test statistic for population mean :-

[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\ z=\dfrac{5.4-5.5}{\dfrac{0.8}{\sqrt{200}}}\approx-1.77[/tex]

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