Question

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 4.1 pounds/square inch (psi). Assume the population standard deviation is 0.6. The engineer designed the valve such that it would produce a mean pressure of 4.2 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

P-value = 0.0046

Explanation:

Given that:

Sample size n = 290

sample mean
`\overline{x_1}` = 4.1

standard deviation
`\sigma` = 0.6

population mean
`\mu` = 4.2

The null and the alternative hypothesis

`\mathbf{H_o: \mu = 4.2} \\ \\ \mathbf{H_a: \mu \\e 4.2}`

This is a two-tailed test.

The test statistics can be computed as:

`Z = (\overline x - \mu )/((\sigma)/(√(n)))`

`Z = (4.1 - 4.2 )/((0.6)/(√(290)))`

`Z = (-0.1 )/((0.6)/(√(290)))`

Z = -2.838

P-value = P(Z> 2.838)

P-value = P(Z< -2.838) +P(Z > 2.838)

P-value = 0.00227 + (1 - 0.9977)

P-value = 0.00457

P-value = 0.0046 (to 4 decimal places)