#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.
H0 : µ = 224 mm
Ha : µ Not = 224 mm
sigma = 0.060 mm given. (the
calculated sample standard deviation = .0618)
n = 16. Std. dev. of xbar = 0.060/4 = 0.015
Calculate xbar = 224.0019375
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
It would be very likely that
we would see a result this far out again.
NO evidence for the alternative.
The results are "consistent with" the null hypothesis being true.
(This test itself doesn't quantify the
evidence FOR the null hypothesis; it wasn't designed to
do so.
To do inference for where the mean IS, do
a Confidence Interval for the true mean, using this data.
The test only judges evidence for where
it ISN'T.)
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