R CLASS EXAMPLES

Exercise 1.11
> library(Devore5)
> data(ex01.11)
> attach(ex01.11)
> mu<-mean(octane)
> sigma<-sd(octane)
>Z<-(octane-mu)/sigma
> mean(Z)
[1] 1.492477e-15
> var(Z)
[1] 1

Exercise 6.02
> library(Devore5)
> data(xmp06.02)
> attach(xmp06.02)
> mean(Voltage)
[1] 27.793
> max(Voltage)
[1] 30.88
> min(Voltage)
[1] 24.46
> (max(Voltage)+min(Voltage))/2
[1] 27.67


Exercise 6.25


> str(ex06.25)
`data.frame':   10 obs. of  1 variable:
 $ strength: int  392 376 401 367 389 362 409 415 358 375
> X<-strength
> M1<-mean(X)
> M2<-sum(X^2)/10
> M1
[1] 384.4
> M2
[1] 148119
> sigma<-sqrt(M2-M1^2)
> sigma
[1] 18.85842

> str(ex06.25)
> x<-strength
> length(x)
[1] 10
> sd(x)
[1] 19.87852
> sigma<-sqrt((length(x)-1)/length(x))*sd(x)
> sigma
[1] 18.85842
> qnorm(0.95,mu,sigma)
[1] 415.4193
> qnorm(0.95)
[1] 1.644854
> pnorm(415,mu,sigma)
[1] 0.9476644
> y<- -30:30/10
> plot(y,dnorm(y),'l')

%Computing confidence intervals
> b<-qnorm(0.975,0,sigma/sqrt(10))
> a<-qnorm(0.025,0,sigma/sqrt(10))
> b
[1] 11.68933
> a
[1] -11.68933
> mean(X)-b
[1] 372.7107
> mean(X)-a
[1] 396.0893

> qnorm(0.995)
[1] 2.575829
> qnorm(0.99)
[1] 2.326348
> qnorm(0.95)
[1] 1.644854
> qnorm(0.975)
[1] 1.959964
> qnorm(0.95)
[1] 1.644854