Rstats.R

pnorm(375,400,70,lower.tail = T) #slide 90

## [1] 0.3604924

qnorm(0.36,mean=400,sd=70) 

## [1] 374.9079

pnorm(375,400,70/10,lower.tail = T) #slide 91

## [1] 0.0001775197

sample(100,10,F)

##  [1] 63 74 52 66 82 67 98 32 48 46

#Simulating a coin flip in R
#Andrew Ellis
#http://rstudio-pubs-static.s3.amazonaws.com/8492_b817c712a5f6456fb4c5932e3d957135.html#/1

sample.space <- c(0,1)
theta <- 0.5 # this is a fair coin
N <- 20 # we want to flip a coin 20 times

flips <- sample(sample.space, 
                size = N, 
                replace = TRUE, 
                prob = c(theta, 1 - theta))

flips

##  [1] 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0

table(flips)

## flips
##  0  1 
## 12  8

barplot(table(flips))

hist(flips,col = rainbow(6))

sample.space2 <- c(1:6)
theta2 <- 1/6 # this is a fair coin
N <- 200 # we want to flip a coin 20 times



rolls <- sample(sample.space2, 
                size = N, 
                replace = TRUE, 
                prob = rep(theta2,6))

rolls

##   [1] 1 6 3 4 2 2 4 6 3 3 1 5 6 4 2 6 1 3 2 6 2 4 4 5 1 4 5 1 6 6 5 5 4 4 4
##  [36] 6 3 6 3 2 4 1 3 2 2 6 3 5 3 6 1 1 2 4 4 1 6 1 1 1 5 4 4 1 2 3 3 5 3 6
##  [71] 1 2 5 6 3 1 6 3 6 3 3 2 5 1 2 5 4 2 4 2 6 4 5 5 2 3 1 1 6 1 3 2 5 2 6
## [106] 5 3 1 1 1 2 6 3 4 4 6 6 6 2 5 4 4 3 6 3 3 5 6 6 6 4 5 6 3 3 4 3 2 2 1
## [141] 6 2 6 2 6 2 3 1 1 5 2 5 1 4 2 3 6 6 6 6 4 4 3 3 3 4 6 2 4 1 3 3 2 3 4
## [176] 3 5 4 1 4 4 5 3 6 6 1 3 6 3 6 2 6 3 4 5 5 3 3 4 3

table(rolls)

## rolls
##  1  2  3  4  5  6 
## 29 30 42 34 24 41

barplot(table(rolls))

hist(rolls,col = rainbow(6))

sample(50,15,F)  #slide120

##  [1] 36 42 49 43 11  8 10 37 39  3 26 31 30 40 46

#slide 52
library(MASS)
height.survey=survey$Height

mean(height.survey,na.rm = T)

## [1] 172.3809

height.response=na.omit(survey$Height)
n=length(height.response)
n

## [1] 209

sigma=9.48
SEmean=sigma/sqrt(n)
SEmean

## [1] 0.6557453

qnorm(0.975)

## [1] 1.959964

E=qnorm(0.975)*SEmean
E

## [1] 1.285237

mean(height.response)

## [1] 172.3809

xbar=mean(height.response)
xbar+c(-E,E)

## [1] 171.0956 173.6661

s=sd(height.response)
SE=s/sqrt(n)
SE

## [1] 0.6811677

Et=qt(0.975,n-1)
Et

## [1] 1.971435

xbar+c(-Et,Et)

## [1] 170.4094 174.3523

sample(c("H","T"),10,T)

##  [1] "T" "T" "H" "T" "T" "H" "H" "H" "H" "T"

dice=as.vector(outer(1:6,1:6,paste))
dice

##  [1] "1 1" "2 1" "3 1" "4 1" "5 1" "6 1" "1 2" "2 2" "3 2" "4 2" "5 2"
## [12] "6 2" "1 3" "2 3" "3 3" "4 3" "5 3" "6 3" "1 4" "2 4" "3 4" "4 4"
## [23] "5 4" "6 4" "1 5" "2 5" "3 5" "4 5" "5 5" "6 5" "1 6" "2 6" "3 6"
## [34] "4 6" "5 6" "6 6"

sample(dice,20,T)

##  [1] "6 6" "5 3" "1 2" "2 1" "5 2" "4 6" "2 3" "1 1" "3 4" "4 2" "5 5"
## [12] "4 1" "4 6" "3 4" "3 5" "2 5" "6 3" "4 1" "2 6" "6 1"