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 51 engines and the mean pressure was 4.4 pounds/square inch with a variance of 0.36. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution :

This is the two tailed test .

Test statistic = z

= ( - ) / / n

= (4.4 - 4.2 / 0.6 / 51

= 2.38

P(z > 2.38) = 1 - P(z < 02.38) = 0.0087

= 0.05

P-value <

Reject the null hypothesis .