Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 270 engines and the mean pressure was 5.6 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 5.5 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 value of the test statistic. Round your answer to two decimal places.

Answer 1

Answer:

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the valve pressure is significantly different from 5.5 psi.

P-value = 0.04

Test statistic z=2.05

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the valve pressure is significantly different from 5.5 psi.

Then, the null and alternative hypothesis are:

$H_0: \mu=5.5\\\\H_a:\mu\neq 5.5$

The significance level is 0.02.

The sample has a size n=270.

The sample mean is M=5.6.

The standard deviation of the population is known and has a value of σ=0.8.

We can calculate the standard error as:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.8}{\sqrt{270}}=0.049$

Then, we can calculate the z-statistic as:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{5.6-5.5}{0.049}=\dfrac{0.1}{0.049}=2.054$

This test is a two-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=2\cdot P(z>2.054)=0.04$

As the P-value (0.04) is bigger than the significance level (0.02), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the valve pressure is significantly different from 5.5 psi.