# 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 5.5 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 variance of 0.49. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

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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 5.5 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 variance of 0.49. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

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Step 1

It is given that sample mean and standard deviation are 8.159 and 0.051, respectively.

The test hypotheses are:

Null hypothesis:

H0: μ = 5.5.

Alternative hypothesis:

H1: μ > 5.5.

Step 2

As the population standard deviation is unknown, the sample standard deviation must be used while performing the test. Thus, the suitable test to use ...

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