strata.samp <- function(df, n)
{
	# strata.samp as function name
	# df and n are passed arguments
	# df is the data frame having the k columns as strata and
	# n is the sample size

	# writing function for the stratified sampling
	# where we need to pass the strata as data frame and
	# sample size as arguments to
	# find the population mean, srs mean, stratified mean,
	# variance of srs mean,
	# variance of stratified sampling mean,
	# standard error of stratified sampling mean and
	# confidence interval of stratified sampling mean

	# finding the number of strata
	k <- ncol(df)

	st.size <- array() # making array of the strata sizes
	pop <- vector() # making a vector of all population

	for (i in 1:k)
	{
		# finding the length of ith stratum
		st.size[i] <- length(na.omit(df[, i]))
		pop <- c(pop, na.omit(df[, i])) # merging the strata
	}

	pop.size <- length(pop) # population size

	samp.st.size <- array() # making array for sample strata sizes
	samp.mean.st <- array() # array of sample means of the strata
	var.samp.st <- array() # array of sample variances of  strata

	for (i in 1:k)
	{
		# finding sample size of ith stratum
		samp.st.size[i] <- round(n * st.size[i] / pop.size)
		# taking sample from ith stratum & storing them to temp
		set.seed(0000)
		temp = sample(na.omit(df[, i]), samp.st.size[i])

		samp.mean.st[i] <- mean(temp) # sample mean of ith stratum
		var.samp.st[i] <- var(temp) # sample variance of ith stratum
	}

	pop.mean <- mean(pop) # population mean

	set.seed(0000)
	srs <- sample(pop, n) # simple random sampling without replacement
	mean.srs <- mean(srs) # finding srs mean

	# finding the variance of srswor mean using formula
	var.srs.mean <- (1 - n / pop.size) * var(srs) / n

	# finding stratified mean
	final.samp.mean.st <- weighted.mean(x = samp.mean.st, w = samp.st.size)

	# finding the variance of stratified sampling mean
	# proportions of the sizes of strata and population size
	w <- st.size / pop.size
	# proportions of sample unit and population unit under strata
	f <- samp.st.size / st.size

	# initialization because we need to
	# increment the variable var.st.mean
	var.st.mean <- 0

	# loop for finding the variance of stratified
	# sampling mean to maintain the iterative sum
	# i is iterative variable

	for (i in 1:k)
	{
		# formula to find the variance of
		# stratified sampling mean

		# passing iterative integer variable i
		# within square brackets
		# which lies between 1 to k
		# to index the arrays

		var.st.mean <- var.st.mean +
			w[i] ^ 2 * (1 - f[i]) * var.samp.st[i] / samp.st.size[i]
	}

	se.st.mean <- sqrt(var.st.mean) # standard error
	margin.err.st.mean <- 1.96 * se.st.mean # margin of error

	# lower value at 95% confidence interval
	lower.confi <- final.samp.mean.st - margin.err.st.mean

	# higher value at 95% confidence interval
	higher.confi <- final.samp.mean.st + margin.err.st.mean

	# 95% confidence interval
	confi.interv <- list("at 95% Lower" = lower.confi,
						 "at 95% Higher" = higher.confi)

	# making the list of all expected answers
	list.results <- list("Population Mean" = pop.mean,
						 "SRS Mean" = mean.srs,
						 "Variance of SRS Mean" = var.srs.mean,
						 "Stratified Sampling Mean" = final.samp.mean.st,
						 "Variance of Stratified Sampling Mean" =
						 	var.st.mean,
						 "Standard Error of Stratified Sampling Mean" =
						 	se.st.mean,
					     "Confidence Interval of Stratified Sampling Mean" =
						 	confi.interv)

	# returning the result as list
	return(list.results)
}

# reading the given csv data as data frame
# dat <- read.csv(file.choose())
dat <- read.csv(file = "hk_sir_stratified_data_25_03_2019.csv")
# dat # printing the data frame

# calling the function by it's name & passing the arguments
strata.samp(dat, 10)

# reference
cat("Coded by\nSFT\n1711024137\nHappy Codding!\n")