Question

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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 7.7 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 210 engines and the mean pressure was 7.9 pounds/square inch. Assume the standard deviation is known to be 1.0. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis.

Answer 1

Sample size = n = 210

Sample mean = = 7.9

Population standard deviation = = 1

The null and alternative hypothesis is

Level of significance = 0.02

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

Critical value = 2.05    ( Using z table)

The critical value < Test statistic z we reject the null hypothesis.

Conclusion:

The valve performs above the specifications.