# 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 7.7 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 7.8 psi, is there sufficient evidence at the 0.01 level that the valve performs below the specifications? Step 1 of 3:State the null and alternative hypotheses.

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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 7.7 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 7.8 psi, is there sufficient evidence at the 0.01 level that the valve performs below the specifications?

Step 1 of 3:

State the null and alternative hypotheses.

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Step 1

Null hypothesis:

µ=7.8.

Alternative hypothesis:

µ<7.8.

Here, the sample mean, x-bar is 7.7.

Population mean, µ is 7.8.

Population variance, σ2 = 0.36.

Population standard deviation, σ = 0.6.

Sample size, n is 160.

The test statistic value can be obtained as follows:

Step 2

Computation of P-value:

The P-value for the z-test for the left tailed z-value –2.108 is 0.00383 which can be can be obtained u...

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### Hypothesis Testing 