# Import the necessary libraries
library("psych")

# Raw data
shoePrices <- c(60,70,75,55,80,55,50,40,80,70,50,95,120,90,75,85,80,60,110,65,80,85,85,45,75,60,90,90,60,95,110,85,45,90,70,70)


mu <- 80 # population mean
sPricesM <- mean(shoePrices) # Mean shoe prices
sigma <- 19.2 # population SD
alpha <- 0.10 # level of significance
n <- 36 # sample size

# Z test
ztest <- (sPricesM - mu)/(sigma/sqrt(n)) 
ztest
# Finding critical value for alpha = 0.05 two-tailed test
cv <- qnorm(alpha, mean = 0, sd = 1, lower.tail = TRUE)
cv

# presented data
mu <- 16.3 # avg population
x  <- 17.7 # avg sample
s  <- 1.8 # sd sample
n  <- 10 # sample size
df <- n-1 # dof
alpha <- 0.05

# t test
ttest <- (x - mu)/(s/sqrt(n))
round(ttest,3)

cv <- qt(alpha/2, df)
round(cv*c(1,-1),3) # critical values

# Presented data
x1 <- 88.42 # avg sample 1
x2 <- 80.61 # avg sample 2
sigma1 <- 5.62 # sd population 1
sigma2 <- 4.83 # sd population 2
n1 <- 50 # sample size 1
n2 <- n1 # sample size 2
alpha <- 0.05 # sig. level

# Calculating Z test
ztest <- ((x1-x2) - 0) / sqrt((sigma1^2/n1) + (sigma2^2/n2))
round(ztest,3)

# Finding critical value for two-tailed test
cv <- qnorm(alpha/2, mean=0, sd = 1)
round(cv*c(1,-1),3)

# Presented data
x1 <- 191
x2 <- 199
n1 <- 8
n2 <- 10
s1 <- 38
s2 <- 12
alpha <- 0.05
df1 <- n1-1
df2 <- n2-1

# Performing t test
ttest <- ((x1-x2) - 0) / sqrt((s1^2/n1) + (s2^2/n2))
round(ttest,3)

# Calculating critical value
if (df1 < df2) {df <- df1} else {df <- df2}

cv <- qt(alpha/2,df)
round(cv*c(1,-1),3)

# Raw data
prior <- c(210,235,208,190,172,244)
after <- c(190,170,210,188,173,228)

n <- 6 # sample size
df <- n-1 # dof
alpha <- 0.1 # sig level
# Calculated data
dM <- mean(prior-after) # avg of differences
sD <- sd(prior-after) # sd of differences

# Statistical test
ttest <- (dM - 0)/(sD/sqrt(n))
round(ttest,3)

# Critical value
cv <- qt(alpha/2,df)
round(cv*c(1,-1),3)