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. The valve was tested on 150 engines and the mean pressure was 4.3 pounds/square inch. Assume the standard deviation is known to be 0.8. Is there evidence at the 0.05 level that the valve performs above the specifications?

Enter the hypotheses

Enter the value of the z test statistic. Round your answer to two decimal places.

Specify if the test is one-tailed or two-tailed.

Enter the decision rule.

Enter the conclusion.

Answer 1

Enter the hypotheses

The hypothesis being tested is:

H₀: µ₁ =4.2

H_a: µ₁ >4.2

Enter the value of the z test statistic. Round your answer to two decimal places.

The test statistic, z = (x - µ)/σ/√n

=(4.3-4.2)/(0.8/√150)= 1.53

Specify if the test is one-tailed or two-tailed.

One tailed [ upper]

Enter the decision rule.

P value=0.0629

Since P value >alpha(0.05). We fail to reject the null hypothesis.

Enter the conclusion.

There is not sufficient evidence to conclude that  the valve performs above the specifications at 5% level of significance.