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.
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.
}
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