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 4.4 pounds/square inch. The valve was tested on 110 engines and the mean pressure was 4.2 pounds/square inch. Assume the standard deviation is known to be 0.7. 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. tep 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.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test:
? : Mean of population
H₀ : ? = 4.4
H_A : ? < 4.4
Standard deviation = 0.7

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
?	110	4.2	0.066742381	-2.9965967	0.0014

Hence,

Step - 1: Hypotheses:

H₀ : ? = 4.4
H_A : ? < 4.4

Step - 2: z test statistic = -3.00

Step - 3: One-tailed

Step - 4: Decision rule: Reject Ho if z < -2.05

Step - 5: Conclusion: Reject the null hypothesis