An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 5.3 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 5.4 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to two decimal places.

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belgrad belgrad · Answer 1 · 2021-01-27T05:05:04+01:00

Answer:

Test statistic Z = 2.1097

Step-by-step explanation:

Step(i):-

Given that size of the sample 'n' = 160

Given that mean of the Population(μ) = 5.3pounds/square inch

The Standard deviation of the population(σ) = 0.6

Mean of the sample(x⁻) = 5.4

Level of significance =0.1

Step(ii):-

Test statistic

[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{5.4-5.3}{\frac{0.6}{\sqrt{160} } }[/tex]

Z = 2.1097

Final answer:-

Test statistic Z = 2.1097