#parts of Chapter 10 excercise 26

iridrhod<-read.table("http://math.cmc.edu/moneill/Math152/Handouts/IRIDRHOD.txt",header=T,na.strings="*")
iridrhod
attach(iridrhod)
Ir<-Ir[!is.na(Ir)]


#stem and leaf

stem(Ir)


#regular plotting

plot(1:length(Ir),Ir)

plot(1:length(Ir),Ir,ylim=c(157,163))

#measures of location

 mean(Ir,trim=.20)

 median(Ir)


#a naive confidence interval

plot(1:length(Ir),Ir,ylim=c(157,163))
lines(c(0,30),c(156.84,156.84))
lines(c(0,30),c(160.785,160.785))



#a non-parametric confidence interval

pbinom(0:27,27,.5)
c(Ir[order(Ir)][10],Ir[order(Ir)][27-10 +1])


#some bootstrapping

#Iridium 20% trimmed mean
d<-replicate(1000,mean(sample(Ir,replace=T),trim=.2))
sd(d)
[1] 0.2828064

#A bootstrap confidence interval

d<-replicate(1000,mean(sample(Ir,replace=T),trim=.2))
thetahat<-mean(Ir,trim=.2)

deltahigh<-d[order(d)][950]-thetahat
deltalow<-d[order(d)][50]-thetahat

c(thetahat-deltahigh,thetahat-deltalow)

#Comparing two samples
#Simulating a rank sum distribution:

f<-function(x){R=sum(sample(1:21,8))

min(R,8*22 -R)}

d<-sapply(1:30000,f)

hist(d)

length(d[d<52])/30000

#Simulating the signed rank test

f<-function(x){sum((1:10)*sample(c(0,1),10,replace=T))}

d<-sapply(1:10000,f)

hist(d)

#chapter 10, problem 48

lottery<-read.table("http://math.cmc.edu/moneill/Math152/Handouts/1970lottery.txt",header=T) 
attach(lottery)

names(lottery)

boxplot(Draft_No~Month_Number)