Question

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 160 engines and the mean pressure was 6.0 pounds/square inch. Assume the variance is known to be 0.36. A level of significance of 0.05 will be used. Determine the decision rule.

Answer 1

Solution:

Given that , = 5.9

Claim : > 5.9 ...(Above specification)

Hypothesis are

H0 : = 5.9  

H1 :   > 5.9

n = 160

= 6.0

² = 0.36 ..(Population variance)

= 0.36 = 0.6    ..(Population Standard deviation)

Use = 0.05 ..level of significance

observe that ,there is > sign in H1. So , the test is right tailed.

So the critical value is i.e. _0.05

i.e. 1.645 (Use z table to find this value)

Decision Rule : Reject H0 if   z >  

i.e. Reject H0 if z >  1.645

{ The test statistic z is given by

z =

= (6.0 - 5.9) / (0.6/160)

= 2.108

z = 2.108 > 1.645

So , We reject H0 at 0.05 level and conclude that there is sufficient evidence to conclude that the valve performs above the specifications.

}