Asked Dec 8, 2019

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.


Expert Answer

Step 1

Null hypothesis:


Alternative hypothesis:


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:


Image Transcriptionclose

z: Vn 7.7 - 7.8 0.6 V160 x -2.108

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...


Image Transcriptionclose

=NORM.S.DIST(-2.108,TRUE) 0.017515495


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