MATH239_HWK3

CallCenter<-read.csv("calls80 copy.csv", 
                     header=TRUE)
head(CallCenter)

##   length
## 1     77
## 2    289
## 3    128
## 4     59
## 5     19
## 6    148

hist(CallCenter$length)

mean(CallCenter$length)

## [1] 196.575

nsim=1000
bootStrapCI1<-function(data, nsim){
  n<-length(data)
  bootCI<-c()
  
  for(i in 1:nsim){
    bootSamp<-sample(1:n, n, replace=TRUE)
    thisXbar<-mean(data[bootSamp])
    bootCI<-c(bootCI, thisXbar)
  }
  return(bootCI)
}

# By hand
xbar<-mean(CallCenter$length) #196.575
sd<-sd(CallCenter$length) #342.0215
sd

## [1] 342.0215

n<-length(CallCenter$length) #80
n

## [1] 80

se<-sd/sqrt(n) #19.32248
se

## [1] 38.23917

mu_0<-130 # One-sided upper alternative I do not know why it is 130

test_stat<-(xbar-mu_0)/se
test_stat #1.74016

## [1] 1.741016

# Bootstrap confidence interval for the mean
lengthBootCI<-bootStrapCI1(CallCenter$length, nsim=1000)

# Approximated sampling distribution
hist(lengthBootCI)

qqnorm(lengthBootCI)
qqline(lengthBootCI)

#10 object sample new bootstrap
###104 102 35 211 56 325 67 9 179 59

SRS<-c(104, 102, 35, 211, 56, 325, 67, 179, 59)


# Function for bootstrap confidence interval 
# for one sample mean
bootStrapCI1<-function(data, nsim){
  n<-length(data)
  bootCI<-c()
  
  for(i in 1:nsim){
    bootSamp<-sample(1:n, n, replace=TRUE)
    thisXbar<-mean(data[bootSamp])
    bootCI<-c(bootCI, thisXbar)
  }
  return(bootCI)
}

# By hand
xbarr<-mean(SRS) #126.44
sdd<-sd(SRS) #94.76565
nn<-length(SRS) #9
see<-sdd/sqrt(nn) #31.59955
mu_00<-130 # One-sided upper alternative 

test_statss<-(xbarr-mu_00)/see 
test_statss #-0.11255

## [1] -0.1125584

SRSBootCI<-bootStrapCI1(SRS, nsim=1000)
# Approximated sampling distribution
hist(SRSBootCI)

qqnorm(SRSBootCI)
qqline(SRSBootCI)

spines<-read.csv("nspines.csv", 
                     header=TRUE)
head(spines)

##   ns  dbh
## 1  n 27.8
## 2  n 14.5
## 3  n 39.1
## 4  n  3.2
## 5  n 58.8
## 6  n 55.5

hist(spines$dbh)

boxplot(spines)

North<-c(27.8, 14.5, 39.1, 3.2, 58.8, 55.5, 25, 5.4, 19, 30.6, 15.1, 3.6, 28.4, 15, 2.2, 14.2, 44.2, 25.7,  11.2,   46.8,   36.9,   54.1,   10.2,   2.5, 13.8,  43.5,   13.8,   39.7,   6.4,    4.8)
South<-c(44.4,  26.1,   50.4,   23.3,   39.5,   51, 48.1,   47.2,   40.3,   37.4,   36.8,   21.7,   35.7,   32, 40.4,   12.8,   5.6,    44.3,   52.9,   38, 2.6,    44.6,   45.5,   29.1,   18.7,   7,  43.8,   28.3,   36.9,   51.6)
qqnorm(North)
qqline(South)

bootStrapCI2<-function(data1, data2, nsim){
  
  n1<-length(data1)
  n2<-length(data2)
  
  bootCI2<-c()
  
  for(i in 1:nsim){
    bootSamp1<-sample(1:n1, n1, replace=TRUE)
    bootSamp2<-sample(1:n2, n2, replace=TRUE)
    thisXbar<-mean(data1[bootSamp1])-mean(data2[bootSamp2])
    bootCI2<-c(bootCI2, thisXbar)
  }
  
  return(bootCI2)
}
spineBootCI<-bootStrapCI2(North, South, nsim=1000)
hist(spineBootCI)

# Quantile Method 
quantile(spineBootCI, c(0.025, 0.975))

##      2.5%     97.5% 
## -19.00375  -3.05625

# Hybrid Method: Parametric critical value and bootstrap SE
bootSE<-sd(spineBootCI)
(mean(North)-mean(South))+c(-1,1)*qt(0.975, df=14)*bootSE

## [1] -19.683923  -1.982744