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 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.

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.

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