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 4.0 pounds/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? is there sufficient or not sufficient evidence?

Answer 1

Solution:

Given ,

= 4.1

claim : = 4.1 or not

Hypothesis are

H0 : = 4.1 (null hypo.)

H1 :     4.1 (Alternative hypothesis)

n = 150

= 4.0

= 0.7

Use = 0.05 significance level.

The test statistic z is given by

z =

= (4.0 - 4.1) / (0.7/150)

= -1.75

Now ,  observe that ,there is   sign in H1. So , the test is two tailed.

For two tailed test ,

p value = 2 * P(Z < -z)

= 2 * P(Z < -1.75)

= 2 * 0.0401

= 0.0802

p value is greater than = 0.05 . So we do not reject the null hypothesis, and conclude that there is not sufficient evidence to conclude that the valve does not perform to the specifications.

Answer :  not sufficient evidence