# This is an example of an R script to calculate the sample size needed
# to estimate the total number of deer pellets in a 20-acre field, as done
# on page 18 of the class notes.  Here, for different choices of the desired
# detectable difference d, the sample size n0 (without the fpc) and n (with
# the fpc) are computed and plotted against the d values.

 N <- 5808                # Defines the population size.
 s2 <- 14.06              # Defines the sample variance.
 z <- qnorm(.975,0,1)     # Defines the standard normal quantile.
 d <- c(1000,1500,2000,2500,3000,# The next two commands are
       3500,4000,4500,5000)      # alternative ways to do the same thing;
 d <- seq(1000,5000,500)         # the "seq" command is very useful here.
 n0 <- N^2*s2*z^2/d^2            # Computes n0, the sample size
                                 # without the fpc.
 n <- 1/(1/n0 + 1/N)             # Computes n, the sample size with the fpc.
 plot(d,n0,xlab="Difference",    # Plots the sample sizes (w/o fpc) versus
  ylab="Sample size",pch=1,      #   the differences (d) with axis labels,
  cex=1.5)                       #   and plotting character 1 (open circle).
                                 #
 points(d,n,pch=16)               # Plots the sample sizes (w/ fpc) versus
                                 #   the differences (d) in overlay, with
                                 #   plotting character 16 (filled circle).
 legend(3000,1500,c("n0","n"),    # Puts a legend on the plot at (2000,6000),
  pch=c(1,16),cex=1.5)           #   using the plotting characters 1 & 16.
 title("Sample Size Required vs. Desired Difference")  # Puts a title on the plot.