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?

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.

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.

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