SOLUTION: A machine produces metal rods used in an automobile suspension system. A random sample of 15 was selected, and the diameter is measured. The sample mean diameter was found to be 8.

Question 1162310: A machine produces metal rods used in an automobile suspension system. A random sample of 15 was selected, and the diameter is measured. The sample mean diameter was found to be 8.24 millimeters. The true standard deviation of the diameters is maintained at σ = 0.02 millimeters. You test if the true mean diameter is significantly lesser than 8.25 millimeters. The P value of the test should be:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The wording is a little unclear.
"The p-value of the test should be"--I assume that one wants to know what it is.
z=(x bar-mean)/sd/sqrt(n)
=-(0.01)/0.02/sqrt (15)
=-(1/2)sqrt (15)
=-1.94
Since we are looking at the lower tail of the z-distribution, we want the probability of z<-1.94, which is the p-value and which is 0.0262.
If alpha, which should be set before the test, is greater than the p-value, then the difference is statistically significant.
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