#   Find the required sample size to force the
#   margin of error to be at a desired level.
#
#   This applies to cases where we know the 
#   population standard deviation.  (Although,
#   if you have at least a rough guess of that,
#   perhaps by looking at the standard deviation
#   of samples from some earlier work then you could
#   adapt this methodology as an approximation even
#   if you did not know the standard deviation of
#   the population.)

#  So, here is a problem.   We know that the
#  standard deviation in the population is 5.36.
#  we want to generate a 97% confidence interval
#  for the population mean.  What sample size 
#  would we need to get the margin of error down
#  to 1.5 or lower?

#  We know that the margin of error is
#  MOE =z_alpha_over_2*pop_sigma/sqrt( samp_size)
#  and if we solve that equation for samp_size 
#  we get 
#  samp_size = (z_alpha_over_2*pop_sigma/MOE)^2
#
#  but for our problem, we know all of the
#  values on the right
z_alpha_over_2 <- qnorm( (1-0.97)/2)
z_alpha_over_2
#
#  so
samp_size <- (z_alpha_over_2*5.36/1.5)^2
samp_size
#  but since you can not get fractional
#  sample sizes we round up so that the MOE 
#  is the desired 1.5 or less.
#  our sample size would be 61.

#
#  Of course we could have used the provided 
#  function, find_samp_size()
source( "../findsampsize.R") # note missing _'s
find_samp_size( 5.36, 0.97, 1.5)