Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.7. If the valve was designed to produce a mean pressure of 4.8 psi, is there sufficient evidence at the 0.05 level that the valve performs above 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

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H₀ : ? = 4.8
H_A : ? > 4.8

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
?	5	0.066742381	109	2.9965967	0.0017

Hence,

Step - 1: Hypotheses:

H₀ : ? = 4.8
H_A : ? > 4.8

Step - 2: Test statistic = 3.00

Step - 3: One - tailed

Step - 4: P - value = 0.0017

Step - 5: Level of significance = 0.05

Step - 6: Reject the null hypothesis