2-sided test:
We measure the probability of seeing something (again) as extreme as the observed value (or more so).
So you need to measure the P-value symmetrically both directions from the observed value--so the P value is double what it would be for a one-sided test.

#6.35, p. 333 Engine crankshafts:  We want to stop the process and fix it if the mean gets too far "off" from 224--either direction would be bad.  So two-sided.     sigma = 0.060 mm.  n = 16.  Std. dev. of xbar = 0.060/4 = 0.015
H0 : mu= 224 mm
Ha : mu Not = 224 mm
Calculate xbar = 224.0019375   (sample standard deviation = .0618)
Standardizing: z = (224.0019375 - 224)/ .015 = .0019375/.015 = 0.12917 ~ .13  (xbar is clearly close to mu)
(If you used .0618, not the .06 you were supposed to, you would get .1254--still rounds to .13)
Farther out than .13 to the right has probability (1- .5517) = .4483.
Farther out than -.13 (symmetrical) to the left also has probability .4483.
So P-value, 2-sided, = .4483 + .4483 = .8966

Sievers home  Math151-Fall02/Crankshafts.htm  11/15/02
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