Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The...

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 4.7 pounds/square inch (psi). Assume the population standard deviation is 0.8. If the valve was designed to produce a mean pressure of 4.5 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

To get full credits, justify your answer by following steps given below. (Upload your work)

Step 1. State the null and alternative hypotheses.

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

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

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

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

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

Homework Answers

Answer #1

Step 1

H0 :- µ = 4.5
H1 :- µ ≠ 4.5

Step 2

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 4.7 - 4.5 ) / ( 0.8 / √( 110 ))
Z = 2.62

Step 3

It is two tailed test

Step 4

P value = 2 * P ( Z > 2.622 ) = 2 * 1 - P ( Z < 2.622 ) = 0.0087 ( From standard normal table )

Step 5

α = 0.02

Step 6

Decision based on P value
Reject null hypothesis if P value < α = 0.02 level of significance
Since 0.0087 < 0.02 ,hence we reject null hypothesis
Result :- Reject null hypothesis

There is sufficient evidence to support the claim that  valve does not perform to the specifications.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110engines and the mean pressure was 4.6 pounds/square inch (psi). Assume the population standard deviation is 0.8 If the valve was designed to produce a mean pressure of 4.5psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? Step 3 of 6: Specify if the test is one-tailed or two-tailed. An engineer...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 150 engines and the mean pressure was 4.0pounds/square inch (psi). Assume the population standard deviation is 0.7 If the valve was designed to produce a mean pressure of 4.1 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? Find the value of the test statistic. Round your answer to two decimal...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines and the mean pressure was 6.5 pounds/square inch (psi). Assume the population variance is 0.64. If the valve was designed to produce a mean pressure of 6.6 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? Step 1 of 6: State the null and alternative hypotheses. Step 2 of...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 7.6 pounds/square inch (psi). Assume the population standard deviation is 1.0. If the valve was designed to produce a mean pressure of 7.7 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? Step 1 of 6: State the null and alternative hypotheses. Step 2...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
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:...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
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:...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 220 engines and the mean pressure was 5.4 pounds/square inch (psi). Assume the population standard deviation is 0.6 . If the valve was designed to produce a mean pressure of 5.5 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? Step 1 of 6: State the null and alternative hypotheses. Step...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 130 engines and the mean pressure was 4.8 pounds/square inch (psi). Assume the population variance is 0.81 If the valve was designed to produce a mean pressure of 4.6psi, is there sufficient evidence at the 0.050.05 level that the valve performs above the specifications? Step 1 of 6: State the null and alternative hypotheses. Step 2 of 6: Find the...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 6.5 pounds/square inch (psi). Assume the population variance is 1.00. If the valve was designed to produce a mean pressure of 6.4 psi, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications? Step 1 of 6 : State the null and alternative hypotheses. An engineer...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The...
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 190 engines and the mean pressure was 6.0 pounds/square inch (psi). Assume the population standard deviation is 0.8. If the valve was designed to produce a mean pressure of 6.1 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? Specify if the test is one-tailed or two-tailed. Find the P-value of...