ZTEST

5.) ZTEST
> TODO: OOo Calc and Gnumeric produce the same results. Excel (2007
> beta) claims to calculate the one-tailed test.
> All produce different results than expected! What OOo Calc and
> Gnumeric calculate is out of my scope. Excel tries to calculate the
> probability by integrating from minus infinity to z and substracts
> this from one. That would only be right, if the absolute value of z is
> taken, not the signed z! (I speak already of the one-tailed results
> for this case, so no confusion here.)
> So, either I made a mistake/misinterpretation or all three apps don't
> get it right(TM)

Well, I'll test it in R. There is NO standard z-test, BUT the t-test
will do it, too. [There is also the package 'TeachingDemos' wich does
define the z-test]

> > z.test(x, mu=15, sd=sd)
>
> One Sample z-test
>
> data: x
> z = 0.3111, n = 30.000, Std. Dev. = 8.803, Std. Dev. of the sample mean
> = 1.607, p-value = 0.7557
> alternative hypothesis: true mean is not equal to 15
> 95 percent confidence interval:
> 12.34980 18.65020
> sample estimates:
> mean of x
> 15.5
where x = 1..30

This same example gives a value of 0.38 in Calc. I have NO idea what
0.38 stands for. And I just noticed that it is impossible to compute a
t-test on a single array in Calc against the expected mean - or did I
miss something?
[The t-test in R gives virtually identical results, because a sample
size of 30 is large enough to approximate the z-distribution.]