Tables of the normal and t-distribution

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The table is available here for download . You are responsible for printing it out and bringing a copy to the final exam.

Run this code in a web-browser to create the normal and t-distribution curves from the above PDF handout.

# The source code used to generate the *normal distribution* section:
q <- c(seq(-3.0, -2.0, 0.25),
c(-1.8, -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 1.8),
seq(2.0, 3.0, 0.25))
cumulative.quantile = pnorm(q)

p <- c(0.001, 0.0025, 0.005, 0.010, 0.025, 0.05, 0.075, 0.10, 0.3, 0.5, 0.7, 0.9, 0.925, 0.950, 0.975, 0.99, 0.995, 0.9975, 0.999)
cumulative.probability = qnorm(p)

layout(matrix(c(1,2), 1, 2))
par(mar=c(4.2, 4.2, 0.2, 1))
plot(q, cumulative.quantile,
type="b",
main="",
xlab="z",
ylab="q = cumulative area under the normal distribution",
cex.lab=1.4,
cex.main=1.8,
lwd=4,
cex.sub=1.8,
cex.axis=1.8,
ylim=c(0, 1))
grid(col="gray30")
a1 = -0.6
arrows(a1, y=-0.2, x1=a1, y1=pnorm(a1), code=0, lwd=2)
arrows(a1, y=pnorm(a1), x1=-3, y1=pnorm(a1), code=2, lwd=2)
text(-2, pnorm(a1)+0.05, "pnorm(z)", cex=1.5)

plot(cumulative.probability, p,
type="b",
main="",
xlab="z",
ylab="q = cumulative area under the normal distribution",
cex.lab=1.4,
cex.main=1.8,
lwd=4,
cex.sub=1.8,
cex.axis=1.8,
ylim=c(0, 1))
grid(col="gray30")
a1 = qnorm(0.65)
arrows(a1, y=0, x1=a1, y1=pnorm(a1), code=1, lwd=2)
arrows(a1, y=pnorm(a1), x1=-5, y1=pnorm(a1), code=0, lwd=2)
text(-2, pnorm(a1)+0.05, "qnorm(q)", cex=1.5)

# The source code used to generate the t-distribution section:

dof <- c(1, 2, 3, 4, 5, 10, 15, 20, 30, 60, Inf)
tail.area.oneside <- c(0.4, 0.25, 0.1, 0.05, 0.025, 0.01, 0.005)

n.dof <- length(dof)
n.tails <- length(tail.area.oneside)

values <- matrix(0, nrow=n.dof, ncol=n.tails)
k=0
for (entry in tail.area.oneside){
k=k+1
values[,k] <- abs(qt(entry, dof))
}
round(values,3)

par(mar=c(4.2, 4.2, 0.2, 1))
z <- seq(-5, 5, 0.01)
probabilty <- dt(z, df=5)
plot(z, probabilty,
type="l",
main="",
xlab="z",
ylab="Probabilities from the t-distribution",
cex.lab=1.4,
cex.main=1.8,
lwd=4,
cex.sub=1.8,
cex.axis=1.8)
abline(h=0)
z=1.5
abline(v=z)
abline(v=0)


The resulting $$t$$-distribution figure was enhanced in Inkscape to add the shaded area.