SOLUTION: A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is Normally Distributed with σ = 0.001 millimeters. A random sample of 15 rings has

Question 1162309: A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is Normally Distributed with σ = 0.001 millimeters. A random sample of 15 rings has a mean diameter of 74.036 millimeters. Test if the true mean ring diameter is significantly greater than 74.035 millimeters.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
With usual assumptions of normality and sd sigma this is a z-test
if alpha 0.05 (not stated) want |z| <1.96
z=((74.036-74.035)/0.001/sqrt(15)
=sqrt(15)=3.87
reject Ho for ring diameter's being 74.036. It is larger.
p-value <0.0001

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