Question

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 places.

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

Find the P-value of the test statistic. Round your answer to four decimal places.

Identify the level of significance for the hypothesis test.

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

Answer #1

**Solution :**

The null and alternative hypothesis are

**H _{0} :
4.1 ........... Null hypothesis**

**H**_{a}**:
**
**4.1 ........... Alternative hypothesis**

Here, n = 150, = 4.0, = 0.7

The test statistic t is

z = **(**
- **
)/[**/n]

= [4.0 - 4.1]/[0.7 /150]

= -1.75

**The value of the test statistic z = -1.75**

Now ,

sign in Ha indicates that the test is TWO TAILED.

z = -1.75

So , using calculator ,

p-value = P(z > 1.75) + P(z < -1.75)

= 0.0401 + 0.0401

**p value = 0.0495**

Since,

p value is greater than the significance level 0.05

Decision:

**Fail to Reject the null hypothesis H0**

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