#Confidence interval of the mean -- multiple approaches. 
#Option 1 is a basic stats function

t.test(Wk06$height, conf.level = 0.95)

## 
##  One Sample t-test
## 
## data:  Wk06$height
## t = 93.838, df = 27, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  64.97606 67.88108
## sample estimates:
## mean of x 
##  66.42857

#Option 2 is the rcompanion approach

#install.packages('rcompanion')
library(rcompanion)

groupwiseMean(height ~ 1, 
              data   = Wk06, 
              conf   = 0.95, 
              digits = 8)

##    .id  n     Mean Conf.level Trad.lower Trad.upper
## 1 <NA> 28 66.42857       0.95   64.97606   67.88108

#Option 3 is from DescTools

MeanCI(Wk06$height,
       conf.level=0.95)

##     mean   lwr.ci   upr.ci 
## 66.42857 64.97606 67.88108

#Option 4 is from Rmisc

#install.packages('Rmisc')
library(Rmisc)

## Loading required package: lattice

CI(Wk06$height,
   ci=0.95)

##    upper     mean    lower 
## 67.88108 66.42857 64.97606

#Groupwise also offers bootstrapped CIs

groupwiseMean(height ~ 1, 
              data   = Wk06, 
              conf   = 0.95, 
              digits = 8,
              R      = 10000,
              boot        = TRUE,
              traditional = FALSE,
              normal      = FALSE,
              basic       = FALSE,
              percentile  = FALSE,
              bca         = TRUE)

##    .id  n     Mean Boot.mean Conf.level Bca.lower Bca.upper
## 1 <NA> 28 66.42857  66.43386       0.95        65     67.75

#Boot also offers bootstrapped confidence intervals

#install.packages('boot')
library(boot)

## 
## Attaching package: 'boot'

## The following object is masked from 'package:lattice':
## 
##     melanoma

Mboot = boot(Wk06$height,
             function(x,i) mean(x[i]), 
             R=10000)

mean(Mboot$t[,1])

## [1] 66.43701

boot.ci(Mboot,
        conf = 0.95, 
        type = c("norm", "basic" ,"perc", "bca")
)

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 10000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = Mboot, conf = 0.95, type = c("norm", "basic", 
##     "perc", "bca"))
## 
## Intervals : 
## Level      Normal              Basic         
## 95%   (65.05, 67.79 )   (65.07, 67.82 )  
## 
## Level     Percentile            BCa          
## 95%   (65.04, 67.79 )   (64.93, 67.71 )  
## Calculations and Intervals on Original Scale