Editing TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/8.2

;Two-sample t-test using normal approximation
Messages are frequently sent from a sender to either receiver 1 or receiver 2. For both receivers, several times for the transfer were measured (in seconds) and stored in the file <code>waitingtimes2.Rdata</code>.
:(a) Plot both data sets. Is their distribution approximately bell-shaped?
:(b) Test the null-hypothesis of equal mean transfer times for both receivers on the 1%-level with a two sample t-test (using the normal approximation).
:(c) Compare your result to the output of <code>t.test()</code>

== Lösungsvorschlag==

a)

<syntaxhighlight lang=r>
load('waitingtimes2.Rdata')
par(mfrow=c(2,1))
x = wt[[1]]
y = wt[[2]]
hist(x)
hist(y)
</syntaxhighlight>

b) 

<syntaxhighlight lang=r>
semx = sd(x)^2/length(x)
semy = sd(y)^2/length(y)

t = (mean(x) - mean(y))/sqrt(semx + semy)
t

pnorm(t)*2
</syntaxhighlight>

c)
<syntaxhighlight lang=r>
t.test(x,y)
</syntaxhighlight>