# Simulate one random sample of n=25
# observations from a standard normal
# distribution
x <- rnorm(25)
x
# Compute the 75-the percentile of
# the sample
y <- quantile(x, 0.75)
y
# Use a single statement to estimate
# the 75-th percentile from a simulated
# sample of 25 observations from a
# standard normal distribution
y <- quantile(rnorm(25), 0.75)
y
# Collect the estimated 75_th percentiles
# for 999 additional simulated samples
# of size 25
for(i in 1:999) {
y <- c(y, quantile(rnorm(25), 0.75) )}
# Construct a histogram
lab <- "1000 upper quartile estimates (n=25)"
hist(y, nclass=20, main=lab)
# Obtain the average of the simulated estimates
mean(y)
# Obtain the standard error of the 1000
# simulated estimates
sqrt(var(y))
# Obtain estimates of the lower 2.5-th percentile and
# and the upper 97.5-th percentile of the distribution
# of the estimates of the upper quartile of a standard
# normal distribution for samples of size 25.
quantile(y, c(0.025, 0.975))
# Compute the true value of the upper quartile
# of a standard normal distribution
qnorm(.75)