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 5.6 pounds/square inch. The valve was tested on 140 engines and the mean pressure was 5.4 pounds/square inch. Assume the variance is known to be 0.81. Is there evidence at the 0.02 level that the valve performs below the specifications?

Step 1 of 5: Enter the hypotheses:

Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places.

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

Step 4 of 5: Enter the decision rule.

Step 5 of 5: Enter the conclusion. Reject or Fail To Reject?

Answer 1

Step 1: Here claim is that mean is below the specifications.

i.e.

As we know null hypothesis always have equality sign, hypothesis here is vs

Step 2. Here xbar=5.4 and standard deviation=0.9

So test statistics is

Step 3. Here alternative hypothesis is having less than sign, so it is one tailed test

Step 4. If P value is less than level of significance we reject the null hypothesis.

Step 5. Here P value is , hence we Reject the null hypothesis