

In [1]:

    
x <- scan("rn01.txt")
x <- sort(x)
n <- length(x)
n









    Out[1]:




40

a)



In [2]:

    
alpha <- 0.05
epsn <- sqrt(1/(2 * n) * log(2/alpha))



In [3]:

    
Fn <- (1:n)/n
plot(x, Fn, type="s", lwd=1, ylab="", xlab="x", main="95% DKW-Konfidenzband")
lower <- pmax(Fn - epsn, 0)
upper <- pmin(Fn + epsn, 1)
conf.b <- cbind(lower, upper)
matplot(x, conf.b, type="s", col=2, add=TRUE)



In [4]:

    
plot(x, Fn, type="s", lwd=1, ylab="", xlab="x", main="95% KS-Konfidenzband")
d <- 1.36/sqrt(n)
lower_ks <- pmax(Fn - d, 0)
upper_ks <- pmin(Fn + d, 1)
conf.b.ks <- cbind(lower_ks, upper_ks)
matplot(x, conf.b.ks, type="s", col=3, add=TRUE)

b)



In [5]:

    
ks.test(x, pnorm)









    Out[5]:





	One-sample Kolmogorov-Smirnov test

data:  x
D = 0.1243, p-value = 0.5263
alternative hypothesis: two-sided

c)



In [6]:

    
require(nortest)
lillie.test(x)









    



Loading required package: nortest






    Out[6]:





	Lilliefors (Kolmogorov-Smirnov) normality test

data:  x
D = 0.10213, p-value = 0.3665



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