Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 150150 engines and the mean pressure was 5.25.2 pounds/square inch (psi). Assume the population standard deviation is 0.90.9. If the valve was designed to produce a mean pressure of 5.35.3 psi, is there sufficient evidence at the 0.020.02 level that the valve performs below the specifications?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Step 1. Here claim is that mean is below 5.3

So hypothesis is vs

Step 2: As population standard deviation is known we will use z statistics

Step 3: As alternative hypothesis is having less than sign it is one tailed test

Step 4: P value is P(z<-1.36)=0.0869

Step 5: Level of significance is alpha=0.02

Step 6: AS P value is greater than alpha we fail to reject the null hypothesis