An engineer has 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 of5.1pounds/square inch. The valve was tested on6engines and the mean pressure was5.5 pounds/square inch with a standard deviation of0.5. Is there evidence at the0.01level that the valve performs above the specifications? Assume the population distribution is approximately normal.

Step 1 of 5:State the null and alternative hypotheses.

Step 2 of 5:Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5:Specify if the test is one-tailed or two-tailed.

Step 4 of 5:Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5:Make the decision to reject or fail to reject the null hypothesis.