# Look at how the half-width of a one-sample confidence interval
# decreases with increasing sample size:
seq(5, 30, by = 5)
#[1] 5 10 15 20 25 30
hw <- ciNormHalfWidth(n.or.n1 = seq(5, 30, by = 5))
round(hw, 2)
#[1] 1.24 0.72 0.55 0.47 0.41 0.37
#----------------------------------------------------------------
# Look at how the half-width of a one-sample confidence interval
# increases with increasing estimated standard deviation:
seq(0.5, 2, by = 0.5)
#[1] 0.5 1.0 1.5 2.0
hw <- ciNormHalfWidth(n.or.n1 = 20, sigma.hat = seq(0.5, 2, by = 0.5))
round(hw, 2)
#[1] 0.23 0.47 0.70 0.94
#----------------------------------------------------------------
# Look at how the half-width of a one-sample confidence interval
# increases with increasing confidence level:
seq(0.5, 0.9, by = 0.1)
#[1] 0.5 0.6 0.7 0.8 0.9
hw <- ciNormHalfWidth(n.or.n1 = 20, conf.level = seq(0.5, 0.9, by = 0.1))
round(hw, 2)
#[1] 0.15 0.19 0.24 0.30 0.39
#==========
# Modifying the example on pages 21-4 to 21-5 of USEPA (2009),
# determine how adding another four months of observations to
# increase the sample size from 4 to 8 will affect the half-width
# of a two-sided 95% confidence interval for the Aldicarb level at
# the first compliance well.
#
# Use the estimated standard deviation from the first four months
# of data. (The data are stored in EPA.09.Ex.21.1.aldicarb.df.)
# Note that the half-width changes from 34% of the observed mean to
# 18% of the observed mean by increasing the sample size from
# 4 to 8.
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
hw.4 <- ciNormHalfWidth(n.or.n1 = 4, sigma.hat = sigma.hat)
hw.4
#[1] 7.852543
hw.8 <- ciNormHalfWidth(n.or.n1 = 8, sigma.hat = sigma.hat)
hw.8
#[1] 4.125688
100 * hw.4/mu.hat
#[1] 33.99369
100 * hw.8/mu.hat
#[1] 17.86012
#==========
# Clean up
#---------
rm(hw, mu.hat, sigma.hat, hw.4, hw.8)
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