Estimating data parameters using R (confidence intervals). Full article at http://www.firsttimeprogrammer.blogspot.com/2015/07/estimating-data-parameters-using-r.html

estimatDataParameters.R

###############################################################################
# Confidence intervals for the population mean (t-student distribution)
# We assume that
# 1. Data is normally distributed
# 2. Samples are iid
#
# Note that population variance is unknown and therefore must be
# estimated. In this case Student distribution should be used.
# The number of degree of freedom is n-1 where n is the size of
# the sample. Note that as n -> Inf the Student distribution tends to
# the Normal distribution.

# Data
data_vector <- c(63, 75, 92, 53, 45, 92, 69, 54, 75, 87)

# Two sided confidence interval (CI)
# a <= mu <= b

two.sided.int <- function(data,alpha)
{
    x <- mean(data)
    sd.mean <- sd(data)
    degree.of.freedom <- length(data)-1
    t.value <- qt(1-alpha/2,degree.of.freedom)
    
    CI <- (sd.mean/sqrt(length(data)))*t.value
    
    confidenceInterval <- c(x-CI,x+CI)
    
    print("Confidence interval for the population mean")
    print(confidenceInterval)
}

# One sided CI
# upper: mu <= c
# lower: mu >= c
one.sided.int <- function(data,alpha,type)
{
    x <- mean(data)
    sd.mean <- sd(data)
    degree.of.freedom <- length(data)-1
    t.value <- qt(1-alpha,degree.of.freedom)
    CI <- (sd.mean/sqrt(length(data)))*t.value
    
    if(type == 'upper'){confidenceInt <- x+CI}
    else if(type == "lower"){confidenceInt <- x-CI}
    else{return(0)}
    
    print(paste(type," bound for the population mean:"))
    print(confidenceInt)
}

one.sided.int(data_vector,0.025,"upper")
one.sided.int(data_vector,0.025,"lower")
two.sided.int(data_vector,0.025)

#############################################################################
# Output
# 
# > one.sided.int(data_vector,0.025,"upper")
# [1] "upper  bound for the population mean:"
# [1] 82.48089
# > one.sided.int(data_vector,0.025,"lower")
# [1] "lower  bound for the population mean:"
# [1] 58.51911
# > two.sided.int(data_vector,0.025)
# [1] "Confidence interval for the population mean"
# [1] 56.27958 84.72042