Question

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 4.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 170 engines and the mean pressure was 4.44 pounds/square inch. Assume the standard deviation is known to be 1.0 A level of significance of 0.02 will be used. Determine the decision.

- How do I find the critical value of Z once the Z test statistic is found? I'm not sure what the process is to finding this number.

- Is the Z test statistic = .766965?

Answer 1

The provided sample mean is 4.44 and the known population standard deviation is σ=1, and the sample size is n = 170

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=4.2

Ha: μ≠​4.2

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.02, and the critical value for a two-tailed test is z_c = 2.33

To find z half the significance level ( 0.02/2 = 0.01 ) as it is two tailed, in case of one tailed , don't.

=NORM.S.INV(0.01)

Use this and value will be obtained

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |z| = 3.129 >zc​=2.33, it is then concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 4.2, at the 0.02 significance level.