Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 180 engines and the mean pressure was 4.8 pounds/square inch (psi). Assume the population standard deviation is 1.0. The engineer designed the valve such that it would produce a mean pressure of 4.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Given:

Sample Size = n = 180

Sample mean = =4.8

thus population standard deviation = =1

Population mean =

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 4.6
Alternative Hypothesis, Ha: μ ≠ 4.6

hence   is known we use Z-test

Find test statistic value:

#value of the test statistic.=2.68