fakedata <- function(size, xbar, sd) {
            if(sd<=0) stop("sd must > 0")
            if(!is.numeric(xbar)) stop("xbar must be a real number")
            fake1 <- rnorm(size)
            fake2 <- fake1 - mean(fake1)
            fake2 * (sd/sd(fake2)) + xbar
}

# In statistical analysis related to student t-test, t-confidence interval,
# often the data was already summurized in terms of sample mean (xbar) and 
# standard deviation (sd) and sample size (size), and no raw data is given. 
# We cannot use R (or Splus) function t.test() since it needs raw data. 
#
# I use the function fakedata to regenerate the (fake) data that match the 
# 1) size, 2) xbar, and 3) sd. For t.test() purposes this will give identical
# results (P-value and confidence interval) as if you had the raw data.
# (Sufficiency!) Written by Mai Zhou mai@ms.uky.edu  4/2000
#
# Example: Suppose a sample of size n=50 had xbar=11.8 and sd=0.6.
# We can get P-value of testing  Ho: mu=12 vs Ha: mu<12    by
# mydata <- fakedata(size=50,xbar=11.8,sd=0.6)
# t.test(mydata, mu=12, alternative="less")