Question

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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 7.3 pounds/square inch (psi). Assume the population variance is 0.81. If the valve was designed to produce a mean pressure of 7.1 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

Answer 1

H0: mu = 7.1

Ha: mu not equasl to 7.1

test statistis:

xbar = 7.3

variance = 0.81

std.dev =sqrt(0.81) = 0.9 , n = 110

z = (xbar - mu)/(sigma/sqrt(n))
= ( 7.3 - 7.1)/(0.9/sqrt(110))
= 2.33

p value = 0.0198

Reject Ho as p value < 0.02

there is sufficient evidence at the 0.02 level that the valve does not perform to the specifications