R help - Nov 2012 - Student-t distributed random value generation within a confidence interval?

Dear R-users!

I?m faced with following problem:
Given is a sample where the sample size is 12, the sample mean is 30, and
standard deviation is 4.1.
Based on a Student-t distribution i?d like to simulate randomly 500 possible
mean values within a two-tailed 95% confidence interval.
Calculation of the lower and upper limit of the two-tailed confidence
interval is the easy part.

m <- 30 #sample mean
s <- 4.1 #standard deviation
n <- 12 #sample size
quant <- qt(0.975,df=11)*s/sqrt(n)#student-t with two tailed )95% confidence
interval
l <- m-quant# lower limit
h <- m+quant# upper limit

500 randomly simulated values are computable with the rt() command but this
command does not consider the 95% confidence interval.

Does somebody of you know, how i can overcome this problem?

Best regards
Thomas




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Thomas Schu <th.schumann <at> gmx.de> writes:
> I?m faced with following problem:
> Given is a sample where the sample size is 12, the sample mean is 30, and
> standard deviation is 4.1.
> Based on a Student-t distribution i?d like to simulate randomly 500
possible
> mean values within a two-tailed 95% confidence interval.
> Calculation of the lower and upper limit of the two-tailed confidence
> interval is the easy part.
> 
> m <- 30 #sample mean
> s <- 4.1 #standard deviation
> n <- 12 #sample size
> quant <- qt(0.975,df=11)*s/sqrt(n)#student-t with two tailed )95%
confidence
> interval
> l <- m-quant# lower limit
> h <- m+quant# upper limit
> 
> 500 randomly simulated values are computable with the rt() command but this
> command does not consider the 95% confidence interval.
  Perhaps: simulate more values than you need and take a subset:

allvals <- rt(1000,df=11)  
## 1000 samples is overkill: slightly more than 
##    500*(1.05) should be large enough
subvals <- (allvals[abs(allvals)<qt(0.975,df=11)])
vals <- m+subvals[1:500]*s/sqrt(n)

I'm subsetting before transforming, it seems slightly easier.