# NOT RUN {
# Look at how the required sample size for a one-sample
# confidence interval decreases with increasing half-width:
seq(0.25, 1, by = 0.25)
#[1] 0.25 0.50 0.75 1.00
ciNormN(half.width = seq(0.25, 1, by = 0.25))
#[1] 64 18 10 7
ciNormN(seq(0.25, 1, by=0.25), round = FALSE)
#[1] 63.897899 17.832337 9.325967 6.352717
#----------------------------------------------------------------
# Look at how the required sample size for a one-sample
# confidence interval increases with increasing estimated
# standard deviation for a fixed half-width:
seq(0.5, 2, by = 0.5)
#[1] 0.5 1.0 1.5 2.0
ciNormN(half.width = 0.5, sigma.hat = seq(0.5, 2, by = 0.5))
#[1] 7 18 38 64
#----------------------------------------------------------------
# Look at how the required sample size for a one-sample
# confidence interval increases with increasing confidence
# level for a fixed half-width:
seq(0.5, 0.9, by = 0.1)
#[1] 0.5 0.6 0.7 0.8 0.9
ciNormN(half.width = 0.25, conf.level = seq(0.5, 0.9, by = 0.1))
#[1] 9 13 19 28 46
#----------------------------------------------------------------
# Modifying the example on pages 21-4 to 21-5 of USEPA (2009),
# determine the required sample size in order to achieve a
# half-width that is 10% of the observed mean (based on the first
# four months of observations) for the Aldicarb level at the first
# compliance well. Assume a 95% confidence level and use the
# estimated standard deviation from the first four months of data.
# (The data are stored in EPA.09.Ex.21.1.aldicarb.df.)
#
# The required sample size is 20, so almost two years of data are
# required assuming observations are taken once per month.
EPA.09.Ex.21.1.aldicarb.df
# Month Well Aldicarb.ppb
#1 1 Well.1 19.9
#2 2 Well.1 29.6
#3 3 Well.1 18.7
#4 4 Well.1 24.2
#...
mu.hat <- with(EPA.09.Ex.21.1.aldicarb.df,
mean(Aldicarb.ppb[Well=="Well.1"]))
mu.hat
#[1] 23.1
sigma.hat <- with(EPA.09.Ex.21.1.aldicarb.df,
sd(Aldicarb.ppb[Well=="Well.1"]))
sigma.hat
#[1] 4.93491
ciNormN(half.width = 0.1 * mu.hat, sigma.hat = sigma.hat)
#[1] 20
#----------
# Clean up
rm(mu.hat, sigma.hat)
# }
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