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 6.8 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 16 engines and the mean pressure was 6.9 pounds/square inch with a variance of 1.0. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution-

form the given information

population standard deviation is unknown and also, sample size is less than 30. So, for test the claim we use t-test.

◆test results and calculations-

where variance = 1.0 so , standard deviation is √1.0 = 1.0

above test results that the null hypothesis Ho is not rejected.

so, there is enough evidence to support the claim that the engineer designed valve such that it would produce mean pressure of 6.8 pounds/square inch

that is valve perform it's specifications.