> # Oskar Hagberg 2012-03-12
> #
> # QUESTION
> #  Is the viscosity at 25C different from 800 iches? In which range may it be?
> #
> # DESCRIPTION OF THE EXPERIMENT
> # To answer the question, 15 batches were collected, and the average computed to:
> xbar = 812
> # PRELIMINARY LOOK AT DATA
> # The average is 12 units separated from 800. The standard deviation is 25. Before 
> # computing, I cannot say if this can be explained by chance alone, but I have a feeling
> # it can-.
> 
> # Since the standard deviation
> # is known, 25 centistokes, we assume the measurements are independend observations of
> # N(mu,15^2). In this setting, we test
> # H0: mu = 800
> # against
> # H1 mu <> 815
> # 
> # DESCRIPTION OF THE ANALYSIS
> # The average diameter is an estimator of mu that has standard error 
> (stderr = 25/sqrt(15))
[1] 6.454972
> # The distance of this estimator to the mean diameter under the null hypothisis is
> (xdist  = xbar-800)
[1] 12
> # which is compared to the standard error:
> (teststat = xdist/(stderr))
[1] 1.859032
> # Since this value is to the right of the origin, and it is appropriate to use a two-sided test
> (p = 2*(1-pnorm(teststat)))
[1] 0.0630226
> # A 95 % confidence interval is <x> +/- 1.96*standard error:
> c(xbar-1.96*stderr,xbar+1.96*stderr)
[1] 799.3483 824.6517
> # This intervals covers 800, even if it is very close, which is in line with 
> # the small still >0.05 P-value
> # Since background data were not given, no model validation can be performed.
>