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An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 6 engines and the mean pressure was 5.4 pounds/square inch with a standard deviation of 0.7. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

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Answer:

Do no reject null hypothesis.  

Conclusion:

there is no sufficient statistical evidence at 0.025 level of significance to support the claim.

Step-by-step explanation:

Given that;

mean x" = 5.4

standard deviation σ = 0.7  

n = 6

Null hypothesis H₀ : μ = 5.0  

Alternative hypothesis H₁ : μ > 5.0    

∝ = 0.025    

now,

t = ( 5.4 - 5.0) / ( 0.7/√6) = 0.4 / 0.2857 = 1.4

degree of freedom df = n-1 = 6 - 1 = 5

T critical = 2.571

Therefore; t < T critical,

Do no reject null hypothesis.  

Conclusion:

there is no sufficient statistical evidence at 0.025 level of significance to support the claim.

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