# NOT RUN {
# Look at how the half-width of a prediction interval increases with
# increasing number of future observations:
1:5
#[1] 1 2 3 4 5
hw <- predIntNormHalfWidth(n = 10, k = 1:5)
round(hw, 2)
#[1] 2.37 2.82 3.08 3.26 3.41
#----------
# Look at how the half-width of a prediction interval decreases with
# increasing sample size:
2:5
#[1] 2 3 4 5
hw <- predIntNormHalfWidth(n = 2:5)
round(hw, 2)
#[1] 15.56 4.97 3.56 3.04
#----------
# Look at how the half-width of a prediction interval increases with
# increasing estimated standard deviation for a fixed sample size:
seq(0.5, 2, by = 0.5)
#[1] 0.5 1.0 1.5 2.0
hw <- predIntNormHalfWidth(n = 10, sigma.hat = seq(0.5, 2, by = 0.5))
round(hw, 2)
#[1] 1.19 2.37 3.56 4.75
#----------
# Look at how the half-width of a prediction interval increases with
# increasing confidence level for a fixed sample size:
seq(0.5, 0.9, by = 0.1)
#[1] 0.5 0.6 0.7 0.8 0.9
hw <- predIntNormHalfWidth(n = 5, conf = seq(0.5, 0.9, by = 0.1))
round(hw, 2)
#[1] 0.81 1.03 1.30 1.68 2.34
#==========
# The data frame EPA.92c.arsenic3.df contains arsenic concentrations (ppb)
# collected quarterly for 3 years at a background well and quarterly for
# 2 years at a compliance well. Using the data from the background well, compute
# the half-width associated with sample sizes of 12 (3 years of quarterly data),
# 16 (4 years of quarterly data), and 20 (5 years of quarterly data) for a
# two-sided 90% prediction interval for k=4 future observations.
EPA.92c.arsenic3.df
# Arsenic Year Well.type
#1 12.6 1 Background
#2 30.8 1 Background
#3 52.0 1 Background
#...
#18 3.8 5 Compliance
#19 2.6 5 Compliance
#20 51.9 5 Compliance
mu.hat <- with(EPA.92c.arsenic3.df,
mean(Arsenic[Well.type=="Background"]))
mu.hat
#[1] 27.51667
sigma.hat <- with(EPA.92c.arsenic3.df,
sd(Arsenic[Well.type=="Background"]))
sigma.hat
#[1] 17.10119
hw <- predIntNormHalfWidth(n = c(12, 16, 20), k = 4, sigma.hat = sigma.hat,
conf.level = 0.9)
round(hw, 2)
#[1] 46.16 43.89 42.64
#==========
# Clean up
#---------
rm(hw, mu.hat, sigma.hat)
# }
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