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

[Liaw, Andy]

> From: 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

I'm going mad!  That should be:

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

Sorry for wasting bw...

Andy

> 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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> > 
>