> # Oskar Hagberg 2012-03-12
> #
> # QUESTION
> # Is the mean diameter different from 0.55 iches?
> #
> # DESCRIPTION OF THE EXPERIMENT
> # To answer the question, 12 shafts vere randomly selected and measured, and their
> # average was computed to 
> xbar = 0.2545
> # Since the standard deviation
> # is known, 0.0001, we assume the measurements are independend observations of
> # N(mu,0.0001^2). In this setting, we test
> # H0: mu = 0.255
> # against
> # H1 mu <> 0.255
> # 
> # DESCRIPTION OF THE ANALYSIS
> # The average diameter is an estimator of mu that has standard error 0.0001/sqrt(12)
> # The distance of this estimator to the mean diameter under the null hypothisis is
> (xdist  = xbar-0.255)
[1] -5e-04
> # which is compared to the standard error:
> (teststat = xdist/(0.0001/sqrt(12)))
[1] -17.32051
> # Since this value is to the left of the origin, 
> # it is appropriate to use this P-value.
> (p = 2*pnorm(teststat))
[1] 3.294362e-67
> # A 95 % confidence interval is <x> +/- 1.96*standard error:
> c(xbar-1.96*0.001/sqrt(12),xbar+1.96*0.001/sqrt(12))
[1] 0.2539342 0.2550658
> # Since background data were not given, no model validation 
> # can be performed.
> 
>