Hypothesis testing on normally distributed data in R. Full article at: http://www.firsttimeprogrammer.blogspot.com/2015/07/hypothesis-testing-on-normally.html

test_hp.R

###############################################################################
# The code below can be used to perform a z-test under the following
# assumptions:
# 1. The data is normally distributed
# 2. Samples are iid
# 
# Remember that:
# 1.Low pvalue: strong empirical evidence against h0
# 2.High pvalue: little or 'no' empirical evidence against h0
#
# Generally, as a rule of thumb pvalue < 0.05 can be considered low 
# however it depends on many factors and I'd rather not dive into 
# this :)

# Data to perform the test on
data_vector <- c(63, 75, 84, 58, 52, 96, 63, 55, 76, 83)

# Left tail test
# H0: mu >= mu0
# H1: mu < mu0
t.test.left <- function(data, mu0, alpha)
{
    t.stat <- (mean(data) - mu0) / (sqrt(var(data) / length(data)))
    dof <- length(data) - 1
    t.critical <- qt(alpha, df= dof) #Es alpha 0.05 -> -1.64 (df=Inf)
    p.value <- pt(t.stat, df= dof)
    
    if(t.stat <= t.critical)
    {
        print("Reject H0")
    }
    else
    {
        print("Accept H0")
    }
    print('T statistic')
    print(t.stat)
    print('T critical value')
    print(t.critical)
    print('P value')
    print(p.value)
    print("#####################")
    
    return(t.stat)
}

t.test.left(data_vector, 73, 0.05)

# Right tail test
# H0: mu <= mu0
# H1: mu > mu0
t.test.right <- function(data, mu0, alpha)
{
    t.stat <- (mean(data) - mu0) / (sqrt(var(data) / length(data)))
    dof <- length(data) - 1
    t.critical <- qt(1-alpha, df= dof) #Es alpha 0.05 -> 1.64 (df=Inf)
    p.value <- 1 - pt(t.stat, df= dof)
    
    if(t.stat >= t.critical)
    {
        print("Reject H0")
    }
    else
    {
        print("Accept H0")
    }
    print('T statistic')
    print(t.stat)
    print('T critical value')
    print(t.critical)
    print('P value')
    print(p.value)
    print("#####################")
    
    return(t.stat)
}

t.test.right(data_vector, 73, 0.05)


# Two tail z test
# H0: mu = mu0
# H1: mu != mu0
t.test.twoTails <- function(data, mu0, alpha)
{
    t.stat <- abs((mean(data) - mu0)) / (sqrt(var(data) / length(data)))
    dof <- length(data) - 1
    t.critical <- qt(1-alpha/2, df= dof) #Es alpha 0.05 -> -1.9599 (df=Inf)
    p.value <- 2*(1-pt(t.stat, df= dof))
    
    if(t.stat >= t.critical)
    {
        print("Reject H0")
    }
    else
    {
        print("Accept H0")
    }
    print('T statistic')
    print(t.stat)
    print('T critical values')
    print(c(-t.critical,t.critical))
    print('P value')
    print(p.value)
    print("#####################")
    
    return(t.stat)
}

t.test.twoTails(data_vector, 73, 0.05)

############################################################################
# Output
# > t.test.left(data_vector, 73, 0.05)
# [1] "Accept H0"
# [1] "T statistic"
# [1] -0.5454726
# [1] "T critical value"
# [1] -1.833113
# [1] "P value"
# [1] 0.2993426
# [1] "#####################"
# [1] -0.5454726
# > t.test.right(data_vector, 73, 0.05)
# [1] "Accept H0"
# [1] "T statistic"
# [1] -0.5454726
# [1] "T critical value"
# [1] 1.833113
# [1] "P value"
# [1] 0.7006574
# [1] "#####################"
# [1] -0.5454726
# > t.test.twoTails(data_vector, 73, 0.05)
# [1] "Accept H0"
# [1] "T statistic"
# [1] 0.5454726
# [1] "T critical values"
# [1] -2.262157  2.262157
# [1] "P value"
# [1] 0.5986851
# [1] "#####################"
# [1] 0.5454726