#  A random sample of n=25 observations 

   x <- c(-19.8, -18.1, -13.9, -10.2, -6.3, -2.7, -2.6, -0.7,
            2.6, 2.9, 4.7, 4.9, 5.1, 5.7, 5.8, 6.0, 6.8, 7.0,
            11.8, 13.0, 15.2, 16.0, 24.2, 26.2, 28.9) 

# Compute sample mean and sample standard deviation

   xmean <- mean(x)
   xmean

   xstd <- sqrt(var(x))
   xstd

# Examine a normal probability plot


frame( )
par(fin=c(8,8),cex=1.4,mex=2.0,lwd=3,pch=2,mkh=0.1)

  qqnorm(x, xlab="Standard normal quantiles",
        ylab="Observations", 
        main="Normal Probability Plot")
  qqline(x)

# Estimate the 75-th percentile

  x75 <- quantile(x, 0.75)
  x75
   

# Obtain 1000 bootstrap replicates of the
# estimate of the 75-the population percentile

 y <- quantile(rnorm(25, xmean, xstd), 0.75)

 for(i in 1:999) {
  y <- c(y, quantile(rnorm(25, xmean, xstd), 0.75) )}


#  Construct a histogram

   par(fin=c(8,8),cex=1.2)
   lab <- "1000 Bootstrap Estimates (n=25)"
   hist(y, nclass=20, main=lab)

#  Obtain the average of the bootstrap replicates

  mean(y)

#  Obtain the standard error of the 1000
#  bootstrap replicates

  sqrt(var(y))

#  Obtain a 95% bootstrap confidence interval
#  for the 75-th percentile of the population 

   quantile(y, c(0.025, 0.975))

#  Report the point estimate of the 75-th
#  percentile of the population

  x75 <- quantile(x, 0.75)
  x75