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 5.6 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 160 engines and the mean pressure was 5.7 pounds/square inch. Assume the variance is known to be 0.25. A level of significance of 0.01 will be used. Make a decision to reject or fail to reject the null hypothesis.

Make a decision.

Answer 1

Given : Sample size=n=160

Sample mean=

Population standard deviation=

Significance level=

Hypothesized value=

Since , the population standard deviation is known and the sample size is greater than 30.

Therefore , use Z-test.

Hypothesis : VS

Here , the test is one ( right ) tailed test.

The value of the test statistic is ,

The critical value is ,

; From standard normal probability table

Rejection region :

Decision : Here , the value of the test statistic is lies in the rejection region.

Therefore , reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to support the claim that the valve performs above the specifications.