TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2023W/HW11.1

Rolling die, part 1

A $d$-sided die with colored sides was rolled $n$ times. The outcomes are stored in the file die.Rdata. (Each side appeared at least once.)

(a) What is $n$? What is $d$?

(b) Visualize the relative frequencies in a colored barplot and add the standard error of each frequency.

(c) Given your graphic, what is your opinion on the assertion: 'the die is fair'?

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Lösung von Tutorin

(a)

# Load data
load(file="die.Rdata")

# Compute statistics
n <- lentgh(w); n
w <- table(w); length(tab)

$n=150$ and $d=4$.

(b)

# Compute statistics
h <- as.vector(tab)/n; h
sem <- sqrt(h*(1-h)/n)

# Make barplot
co <- c("blue", "orange", "red", "green")
bar <- barplot(tab/n, col=co, main="Relative Häufigkeiten (n=150)", ylim=c(0, max(h+sem)), las=1)
b <- as.vector(bar)
arrows(bar, h-sem, bar, h+sem, code=3, col="darkgoldenrod", length=0.1, angle=90, lwd=3, xpd=TRUE)

(c)

It is very typical to observe the corresponding frequencies if the dice is fair (standard error: 'The frequencies are partly far apart')