[R] Stats Question: Single data item versus Sample from Norma l Distribution

[Liaw, Andy]

> From: Liaw, Andy 
> 
> Here's one possibility, assuming muhat and sigmahat are 
> estimtes of mu and sigma from N iid draws of N(mu, sigma^2):
> 
> tStat <- abs(x - muhat) / sigmahat
> pValue <- pt(tStat, df=N, lower=TRUE)

Oops...  That should be:

pValue <- pt(tStat, df=N, lower=TRUE) / 2

Andy

> 
> I'm not quite sure what df tStat should have (exercise for 
> math stat), but given fairly large N, that should make little 
> difference.
> 
> Andy
> 
> > From: Ross Clement
> > 
> > Hi. I have a question that I have asked in other stat forums 
> > but do not
> > yet have an answer for. I would like to know if there is 
> some way in R
> > or otherwise of performing the following hypothesis test.
> > 
> > I have a single data item x. The null hypothesis is that x 
> > was selected
> > from a normal distribution N(mu,sigma). The alternate 
> > hypothesis is that
> > x does not come from this distribution.
> > 
> > However, I do not know the values of mu and sigma. I have a 
> sample of
> > size N from which I can estimate mu and sigma. So, say that I have
> > N(m,s,N), and x. I would like to say with some certainty 
> > (e.g. 95%) that
> > I can, or can't reject the hypothesis that x came from 
> N(mu,sigma). I
> > would also like a power test to say how large N should be given the
> > degree of accuracy I need when accepting or rejecting individual x
> > values.
> > 
> > What is the name of the hypothesis test I need for this? Is it built
> > into R, or are there packages I could use?
> > 
> > Thanks in anticipation,
> > 
> > Ross Clement.
> > 
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>