Question

# An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer...

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 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 5.7 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.05 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.

Solution :

Given that ,

= 5.4

= 5.7

= 1.0

n = 24

The null and alternative hypothesis is ,

H0 :   = 5.4

Ha : > 5.4

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 5.7 - 5.4 ) / 1.0 / 24

= 1.47

The test statistic = 1.47

P -value = P ( Z > 1.74 ) = 1- P ( Z < 1.47 )

= 1 - 0.9292

= 0.0708

P-value = 0.071

= 0.05

0.071 > 0.05

P-value >

Fail to reject the null hypothesis .

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